{"version":3,"file":"_Pavages_et_transformations-jEyFTTB5.js","sources":["../../src/exercices/6e/_Pavages_et_transformations.js"],"sourcesContent":["import { codageAngleDroit } from '../../lib/2d/angles.js'\nimport { arc } from '../../lib/2d/cercle.js'\nimport { codageSegments } from '../../lib/2d/codages.js'\nimport { droiteHorizontaleParPoint, droiteVerticaleParPoint, mediatrice } from '../../lib/2d/droites.js'\nimport { milieu, point, pointIntersectionDD, pointSurDroite, tracePoint } from '../../lib/2d/points.js'\nimport { barycentre, polygone } from '../../lib/2d/polygones.js'\nimport { segment, vecteur } from '../../lib/2d/segmentsVecteurs.js'\nimport { labelPoint, latexParCoordonnees, texteParPoint } from '../../lib/2d/textes.js'\nimport { rotation, similitude, translation } from '../../lib/2d/transformations.js'\nimport { choice } from '../../lib/outils/arrayOutils'\nimport { miseEnEvidence, texteEnCouleurEtGras } from '../../lib/outils/embellissements'\nimport { numAlpha } from '../../lib/outils/outilString.js'\nimport FractionEtendue from '../../modules/FractionEtendue.js'\nimport { imagePointParTransformation } from '../../modules/imagePointParTransformation.js'\nimport Exercice from '../Exercice.js'\nimport { assombrirOuEclaircir, colorToLatexOrHTML, fixeBordures, mathalea2d } from '../../modules/2dGeneralites.js'\nimport { context } from '../../modules/context.js'\nimport { egal, gestionnaireFormulaireTexte, listeQuestionsToContenuSansNumero, randint } from '../../modules/outils.js'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.js'\nimport { rotationAnimee, symetrieAnimee, translationAnimee } from '../../modules/2dAnimation.js'\nimport { setReponse } from '../../lib/interactif/gestionInteractif.js'\n\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\nexport const amcReady = true\nexport const amcType = 'AMCHybride'\n/**\n * Trouver l'image d'une figure par diverses transformations dans un pavage (7 motifs différents)\n * @author Jean-Claude Lhote\n * fonction servant à tous les niveaux\n * Références 5G12-1, 6G25-2, 4G11-1, 3G12-1\n * Relecture : Novembre 2021 par EE\n */\nexport default function PavagesEtTransformations () {\n  Exercice.call(this) // Héritage de la classe Exercice()\n\n  // this.title = \"Find the image of a figure by central symmetry\";\n  this.consigne = ''\n  this.nbQuestions = 1\n  this.nbQuestionsModifiable = false\n  this.nbCols = 1\n  this.nbColsCorr = 1\n  this.listeAvecNumerotation = false\n  this.besoinFormulaire2Texte = ['Choice of pavings', 'Numbers separated by hyphens\\nChoice between 1 and 7\\nChoice 8 for a mix of all tilings']\n  this.sup2 = 8\n  // this.sup = 1 // 1 for axial symmetry, 2 for central symmetry, 3 for translations, and 4 for rotations; parameter set by the respective variants.\n  // context.isHtml ? this.spacingCorr = 2.5: this.spacingCorr = 1.5\n  this.nouvelleVersion = function (numeroExercice) {\n    this.listeQuestions = []\n    this.listeCorrections = [] // Liste de questions corrigées\n    const typeDePavage = gestionnaireFormulaireTexte({\n      max: 7,\n      defaut: 8,\n      melange: 8,\n      nbQuestions: this.nbQuestions,\n      saisie: this.sup2\n    })\n    const objetsEnonce = []\n    const objetsCorrection = []\n    if (this.level === 3) {\n      this.sup = 4\n    } else if (this.level === 4) {\n      this.sup = 3\n    } else if (this.level === 5) {\n      this.sup = 2\n    } else this.sup = 1\n    // lists of tilings [nx,ny,xB,yB,xC,yC,xD,yD,zoom,angle]: 0=squares, 1=kite 2=quadri concave 3=quadri any 4=parallelograms 5=triangles isosceles rectangles 6=equilateral triangles 7=rhombuses\n    const paves = [[5, 5, 4, 0, 4, 4, 0, 4, 30, 0], [5, 5, 6, 0, 8, 8, 0, 6, 60, -9], [5, 5, 8, 0, 4, 4, 2, 8, 50, 0], [5, 5, 4, 0, 6, 4, 0, 6, 50, 5], [4, 6, 8, 0, 7, 4, -1, 4, 50, 10], [5, 5, 8, 0, 4, 4, 0, 8, 50, 0], [5, 5, 4, 0, 3, 2 * Math.sin(Math.PI / 3), 2, 4 * Math.sin(Math.PI / 3), 20, 0], [4, 4, 3, 1, 4, 4, 1, 3, 20, 0]]\n    const quad = []\n    const quadCorr = []\n    let labelCentre1, labelCentre2, labelCentre3\n    let quad1\n    let quad2\n    let quad3\n    let mediatrice1, mediatrice2, mediatrice3, centre1, centre2, centre3, arc1, arc2, arc3, rayon11, rayon12,\n      rayon21, rayon22, rayon31, rayon32\n    let vecteur1, vecteur2, vecteur3, vector1, vector2, vector3, origine1, origine2, origine3, indexsym2, indexsym1,\n      indexsym3\n    let segCorr11, segCorr12, segCorr21, segCorr22, segCorr31, segCorr32\n    let B, C, D\n    let iB1, iB2, iB3, iC1, iA1, iD1\n    let texte = ''\n    let texteCorr = ''\n    const tabfigA = []\n    const tabfigB = []\n    const tabfigC = []\n    const tabfigD = []\n    let pave = []\n    let choixPave\n    switch (this.sup) {\n      case 1:\n        choixPave = 0 // pavages adaptés à symétrie axiale (carrés)\n        break\n      case 2:\n        // choicePave = randint(0, 7)// tilings adapted to central symmetry (all)\n        choixPave = typeDePavage[0]// pavages adaptés à symétrie centrale (tous)\n        break\n      case 3:\n        choixPave = randint(0, 7) // pavages adaptés à translation (tous)\n        break\n      case 4:\n        choixPave = 0 // pavages adaptés à rotation (carrés)\n        break\n    }\n    pave = paves[choixPave]\n\n    const nx = pave[0]\n    const ny = pave[1]\n    let xB = pave[2]\n    let yB = pave[3]\n    let xC = pave[4]\n    let yC = pave[5]\n    let xD = pave[6]\n    let yD = pave[7]\n    const Zoom = pave[8]\n    const Angle = pave[9]\n    const A = point(0, 0)\n    if (choixPave !== 0 && choixPave !== 6 && choixPave !== 7) {\n      B = similitude(point(xB, yB), A, Angle, 22 / Zoom)\n      C = similitude(point(xC, yC), A, Angle, 22 / Zoom)\n      D = similitude(point(xD, yD), A, Angle, 22 / Zoom)\n      xB = B.x\n      yB = B.y\n      xC = C.x\n      yC = C.y\n      xD = D.x\n      yD = D.y\n    } else {\n      B = point(xB, yB)\n      C = point(xC, yC)\n      D = point(xD, yD)\n    }\n    const xAI = xB + xC - xD\n    const yAI = yB + yC - yD\n    const I = milieu(B, C)\n    const J = milieu(D, C)\n    const xAJ = xC + xD - xB\n    const yAJ = yC + yD - yB\n    let xAxy, yAxy, numAxy\n    let punto = [0, 0, 0]\n    let trouver = false\n    let indexA\n    let numA\n    let indexcentre1\n    let xmil1 = 0\n    let ymil1 = 0\n    let indexD\n    let numD\n    let indexcentre2\n    let xmil2 = 0\n    let ymil2 = 0\n    let indexC\n    let numC\n    let indexcentre3\n    let xmil3 = 0\n    let ymil3 = 0\n    let num1\n    let num2\n    let num3\n    let xc = 0\n    let yc = 0\n    let xb = 0\n    let yb = 0\n    let xa = 0\n    let ya = 0\n    let xV1 = 0\n    let yV1 = 0\n    let xV2 = 0\n    let yV2 = 0\n    let xV3 = 0\n    let yV3 = 0\n    const s0 = choice(['S', 'T', 'L', 'W', 'R', 'G', 'E', 'F', 'G', 'K'])\n    const s1 = choice(['S', 'T', 'L', 'W', 'R', 'G', 'E', 'F', 'G', 'K'], [s0])\n    const s2 = choice(['S', 'T', 'L', 'W', 'R', 'G', 'E', 'F', 'G', 'K'], [s0, s1])\n    const Xmin = Math.min(-1, ny * xAJ)\n    const Xmax = Math.max(nx * xAI + 1, nx * xAI + ny * xAJ + 1)\n    const Ymin = Math.min(-1, nx * yAI)\n    const Ymax = Math.max(nx * yAI + ny * yAJ + 1, ny * yAJ + 1)\n\n    for (let y = 0; y < ny; y++) { // On initialise les tableaux avec les coordonnées des puntos de référence (A,B,C et D) de chaque translaté et son numéro dans le pavage.\n      for (let x = 0; x < nx; x++) {\n        xAxy = new FractionEtendue(Math.round((x * xAI + y * xAJ) * 100), 100)\n        yAxy = new FractionEtendue(Math.round((x * yAI + y * yAJ) * 100), 100)\n        numAxy = 2 * x + 4 * y * nx\n        tabfigA.push([xAxy, yAxy, numAxy])\n        quad[numAxy] = translation(polygone(A, B, C, D), vecteur(xAxy, yAxy))\n        quadCorr[numAxy] = translation(polygone(A, B, C, D), vecteur(xAxy, yAxy))\n        tabfigB.push([xAxy.sommeFraction(new FractionEtendue(Math.round(xB * 100), 100)), yAxy.sommeFraction(new FractionEtendue(Math.round(yB * 100), 100)), numAxy + 1])\n        quad[numAxy + 1] = translation(rotation(polygone(A, B, C, D), I, 180), vecteur(xAxy, yAxy))\n        quadCorr[numAxy + 1] = translation(rotation(polygone(A, B, C, D), I, 180), vecteur(xAxy, yAxy))\n        tabfigD.push([xAxy.sommeFraction(new FractionEtendue(Math.round(xD * 100), 100)), yAxy.sommeFraction(new FractionEtendue(Math.round(yD * 100), 100)), numAxy + 2 * nx])\n        quad[numAxy + 2 * nx] = translation(rotation(polygone(A, B, C, D), J, 180), vecteur(xAxy, yAxy))\n        quadCorr[numAxy + 2 * nx] = translation(rotation(polygone(A, B, C, D), J, 180), vecteur(xAxy, yAxy))\n        tabfigC.push([xAxy.sommeFraction(new FractionEtendue(Math.round(xC * 100), 100)), yAxy.sommeFraction(new FractionEtendue(Math.round(yC * 100), 100)), numAxy + 2 * nx + 1])\n        quad[numAxy + 2 * nx + 1] = translation(translation(polygone(A, B, C, D), vecteur(A, C)), vecteur(xAxy, yAxy))\n        quadCorr[numAxy + 2 * nx + 1] = translation(translation(polygone(A, B, C, D), vecteur(A, C)), vecteur(xAxy, yAxy))\n      }\n    }\n    for (let i = 0; i < quad.length; i++) {\n      objetsEnonce.push(quad[i], texteParPoint(i, barycentre(quad[i], '', 'center'), 'medium', 'black', 1, 'middle', false))\n      quadCorr[i].color = colorToLatexOrHTML(assombrirOuEclaircir('gray', 50))\n      objetsCorrection.push(quadCorr[i], texteParPoint(i, barycentre(quad[i], '', 'center'), 'medium', assombrirOuEclaircir('gray', 50), 1, 'middle', false))\n    }\n\n    context.fenetreMathalea2d = [Xmin, Ymin, Xmax, Ymax]\n    let trace, label, pt1, pt2\n    let texteAMC1, texteAMC2, texteAMC3, consigneAMC\n    switch (parseInt(this.sup)) {\n      case 1: // symétrie axiale\n        // First question: a type A figure by axis symmetry // at [BD] is a type A figure. the symmetric of vertex A is vertex C\n        indexA = randint(0, nx * ny - 1)\n        numA = tabfigA[indexA][2]\n        indexsym1 = randint(0, nx * ny - 1, [indexA]) // sert à choisir un axe [BD].\n        xmil1 = tabfigD[indexsym1][0] // sert pour faire passer l'axe de symétrie.\n        ymil1 = tabfigD[indexsym1][1]\n        punto = imagePointParTransformation(2, [tabfigA[indexA][0], tabfigA[indexA][1]], [xmil1, ymil1])\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigC[j][0], 0.001) && egal(punto[1], tabfigC[j][1], 0.001)) {\n              trouver = true\n              num1 = tabfigA[j][2]\n              xa = tabfigA[indexA][0]\n              ya = tabfigA[indexA][1]\n              mediatrice1 = mediatrice(point(xa, ya), point(punto[0], punto[1]))\n              mediatrice1.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n              mediatrice1.epaisseur = 2\n              mediatrice1.isVisible = true\n              segCorr11 = segment(point(xa, ya), milieu(point(xa, ya), point(punto[0], punto[1])), context.isAmc ? 'black' : 'green')\n              segCorr12 = segment(point(punto[0], punto[1]), milieu(point(xa, ya), point(punto[0], punto[1])), context.isAmc ? 'black' : 'green')\n              segCorr11.epaisseur = 2\n              segCorr11.pointilles = 2\n              segCorr12.epaisseur = 2\n              segCorr12.pointilles = 2\n              objetsCorrection.push(codageAngleDroit(pointSurDroite(mediatrice1, 1), milieu(point(xa, ya), point(punto[0], punto[1])), point(xa, ya), context.isAmc ? 'black' : 'green', 0.8, 1))\n              quad[numA].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n              quad[numA].opaciteDeRemplissage = 0.6\n              break\n            }\n          }\n          if (trouver === false) {\n            indexA = randint(0, nx * ny - 1)\n            numA = tabfigA[indexA][2]\n            indexsym1 = randint(0, nx * ny - 1, [indexA])\n            xmil1 = tabfigD[indexsym1][0]\n            ymil1 = tabfigD[indexsym1][1]\n            punto = imagePointParTransformation(2, [tabfigA[indexA][0], tabfigA[indexA][1]], [xmil1, ymil1])\n          }\n        }\n        texteAMC1 = numAlpha(0) + ' What is the number of the symmetrical figure of the figure ' + texteEnCouleurEtGras(`${numA}`, context.isAmc ? 'black' : 'green') + ` in $${miseEnEvidence('(d_1)', context.isAmc ? 'black' : 'green')}$ axis symmetry?` + ajouteChampTexteMathLive(this, 0, 'width25 inline') + '<br>'\n        texte += texteAMC1\n        texteCorr += numAlpha(0) + ' The symmetrical figure of the figure ' + texteEnCouleurEtGras(`${numA}`, context.isAmc ? 'black' : 'green') + ` in axis symmetry $${miseEnEvidence('(d_1)', context.isAmc ? 'black' : 'green')}$ has the number ${texteEnCouleurEtGras(num1)}.<br>`\n\n        // Second question: a type D figure by axis symmetry // at [AC] is a type B figure. the symmetric of vertex B is vertex D\n        indexD = randint(0, nx * ny - 1)\n        numD = tabfigD[indexD][2]\n        indexsym2 = randint(0, nx * ny - 1, [indexD]) // sert à choisir un axe [AC].\n        xmil2 = tabfigA[indexsym2][0] // sert pour faire passer l'axe de symétrie.\n        ymil2 = tabfigA[indexsym2][1]\n        punto = imagePointParTransformation(1, [tabfigD[indexD][0], tabfigD[indexD][1]], [xmil2, ymil2])\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigB[j][0], 0.001) && egal(punto[1], tabfigB[j][1], 0.001)) {\n              trouver = true\n              num2 = tabfigB[j][2]\n              xb = tabfigD[indexD][0]\n              yb = tabfigD[indexD][1] - 4\n              mediatrice2 = mediatrice(point(xb, yb + 4), point(punto[0], punto[1]))\n              mediatrice2.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n              mediatrice2.epaisseur = 2\n              mediatrice2.isVisible = true\n              segCorr21 = segment(point(xb, yb + 4), milieu(point(xb, yb + 4), point(punto[0], punto[1])), context.isAmc ? 'black' : 'red')\n              segCorr22 = segment(point(punto[0], punto[1]), milieu(point(xb, yb + 4), point(punto[0], punto[1])), context.isAmc ? 'black' : 'red')\n              segCorr21.epaisseur = 2\n              segCorr21.pointilles = 2\n              segCorr22.epaisseur = 2\n              segCorr22.pointilles = 2\n              objetsCorrection.push(codageAngleDroit(pointSurDroite(mediatrice2, 1), milieu(point(xb, yb + 4), point(punto[0], punto[1])), point(xb, yb + 4), context.isAmc ? 'black' : 'red', 0.8, 1))\n              quad[numD].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n              quad[numD].opaciteDeRemplissage = 0.6\n\n              break\n            }\n          }\n          if (trouver === false) {\n            indexD = randint(0, nx * ny - 1)\n            numD = tabfigD[indexD][2]\n            indexsym2 = randint(0, nx * ny - 1, [indexD]) // sert à choisir un axe [AC].\n            xmil2 = tabfigA[indexsym2][0] // sert pour faire passer l'axe de symétrie.\n            ymil2 = tabfigA[indexsym2][1]\n            punto = imagePointParTransformation(1, [tabfigD[indexD][0], tabfigD[indexD][1]], [xmil2, ymil2])\n          }\n        }\n        texteAMC2 = numAlpha(1) + 'What is the number of the symmetrical figure of the figure ' + texteEnCouleurEtGras(`${numD}`, context.isAmc ? 'black' : 'red') + ` in $${miseEnEvidence('(d_2)', context.isAmc ? 'black' : 'red')}$ axis symmetry?` + ajouteChampTexteMathLive(this, 1, 'width25 inline') + '<br>'\n        texte += '<br>' + texteAMC2\n        texteCorr += '<br>' + numAlpha(1) + ' The symmetrical figure of the figure ' + texteEnCouleurEtGras(`${numD}`, context.isAmc ? 'black' : 'red') + ` in axis symmetry $${miseEnEvidence('(d_2)', context.isAmc ? 'black' : 'red')}$ has the number ${texteEnCouleurEtGras(num2)}.<br>`\n\n        // third question: a type D figure by axis symmetry // at [DC] is a type A figure. the symmetric of vertex D is vertex A'\n        indexC = randint(0, nx * ny - 1)\n        numC = tabfigC[indexC][2]\n        indexsym3 = randint(0, 4, Math.floor(indexC / 5)) * 5 // sert à choisir un axe [AC].\n        xmil3 = tabfigC[indexsym3][0] // sert pour faire passer l'axe de symétrie.\n        ymil3 = tabfigC[indexsym3][1]\n        punto = imagePointParTransformation(3, [tabfigC[indexC][0], tabfigC[indexC][1]], [xmil3, ymil3])\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigC[j][0], 0.001) && egal(punto[1], tabfigC[j][1], 0.001)) {\n              trouver = true\n              num3 = tabfigB[j][2]\n              xc = tabfigC[indexC][0]\n              yc = tabfigC[indexC][1]\n              mediatrice3 = mediatrice(point(xc, yc), point(punto[0], punto[1]))\n              mediatrice3.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n              mediatrice3.epaisseur = 2\n              mediatrice3.isVisible = true\n              segCorr31 = segment(point(xc, yc), milieu(point(xc, yc), point(punto[0], punto[1])), context.isAmc ? 'black' : 'blue')\n              segCorr32 = segment(point(punto[0], punto[1]), milieu(point(xc, yc), point(punto[0], punto[1])), context.isAmc ? 'black' : 'blue')\n              segCorr31.epaisseur = 2\n              segCorr31.pointilles = 2\n              segCorr32.epaisseur = 2\n              segCorr32.pointilles = 2\n              objetsCorrection.push(codageAngleDroit(pointSurDroite(mediatrice3, 1), milieu(point(xc, yc), point(punto[0], punto[1])), point(xc, yc), context.isAmc ? 'black' : 'blue', 0.8, 1))\n              quad[numC].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n              quad[numC].opaciteDeRemplissage = 0.6\n              break\n            }\n          }\n          if (trouver === false) {\n            indexC = randint(0, nx * ny - 1)\n            numC = tabfigC[indexC][2]\n            const indexsym3 = randint(0, 4, Math.floor(indexC / 5)) * 5 // sert à choisir un axe [AC].\n            xmil3 = tabfigC[indexsym3][0] // sert pour faire passer l'axe de symétrie.\n            ymil3 = tabfigC[indexsym3][1]\n            punto = imagePointParTransformation(3, [tabfigC[indexC][0], tabfigC[indexC][1]], [xmil3, ymil3])\n          }\n        }\n        texteAMC3 = numAlpha(2) + ' What is the number of the symmetrical figure of the figure ' + texteEnCouleurEtGras(`${numC}`, context.isAmc ? 'black' : 'blue') + ` in $${miseEnEvidence('(d_3)', context.isAmc ? 'black' : 'blue')}$ axis symmetry?` + ajouteChampTexteMathLive(this, 2, 'width25 inline') + '<br>'\n        texte += '<br>' + texteAMC3\n        texteCorr += '<br>' + numAlpha(2) + ' The symmetrical figure of the figure ' + texteEnCouleurEtGras(`${numC}`, context.isAmc ? 'black' : 'blue') + ` in axis symmetry $${miseEnEvidence('(d_3)', context.isAmc ? 'black' : 'blue')}$ has the number ${texteEnCouleurEtGras(num3)}.<br>`\n\n        objetsEnonce.push(mediatrice1, mediatrice2, mediatrice3)\n        objetsCorrection.push(mediatrice1, mediatrice2, mediatrice3, symetrieAnimee(quad[numA], mediatrice1, `id=\"anim${numeroExercice}A\" hard=\"2s\" repeatcount=\"1\"`), symetrieAnimee(quad[numD], mediatrice2, `id=\"anim${numeroExercice}B\" dur=\"2s\" repeatcount=\"1\"`), symetrieAnimee(quad[numC], mediatrice3, `id=\"anim${numeroExercice}C\" dur=\"2s\" repeatcount=\"1\"`))\n\n        pt1 = pointIntersectionDD(mediatrice1, droiteHorizontaleParPoint(point(context.fenetreMathalea2d[2], context.fenetreMathalea2d[3])))\n        pt2 = pointIntersectionDD(mediatrice1, droiteVerticaleParPoint(point(context.fenetreMathalea2d[0], context.fenetreMathalea2d[1])))\n        if (pt1.x > pt2.x) {\n          objetsEnonce.push(latexParCoordonnees('(d_1)', pt1.x, pt1.y - 2.5, context.isAmc ? 'black' : 'green', 20, 10, '', 12))\n          objetsCorrection.push(latexParCoordonnees('(d_1)', pt1.x, pt1.y - 2.5, context.isAmc ? 'black' : 'green', 20, 10, '', 12))\n        } else {\n          objetsEnonce.push(latexParCoordonnees('(d_1)', pt2.x + 2.5, pt2.y, context.isAmc ? 'black' : 'green', 20, 10, '', 12))\n          objetsCorrection.push(latexParCoordonnees('(d_1)', pt2.x + 2.5, pt2.y, context.isAmc ? 'black' : 'green', 20, 10, '', 12))\n        }\n\n        pt1 = pointIntersectionDD(mediatrice2, droiteHorizontaleParPoint(point(context.fenetreMathalea2d[0], context.fenetreMathalea2d[1])))\n        pt2 = pointIntersectionDD(mediatrice2, droiteVerticaleParPoint(point(context.fenetreMathalea2d[0], context.fenetreMathalea2d[1])))\n        if (pt1.x > pt2.x) {\n          objetsEnonce.push(latexParCoordonnees('(d_2)', pt1.x, pt1.y + 2.5, context.isAmc ? 'black' : 'red', 20, 10, '', 12))\n          objetsCorrection.push(latexParCoordonnees('(d_2)', pt1.x, pt1.y + 2.5, context.isAmc ? 'black' : 'red', 20, 10, '', 12))\n        } else if (pt1.x < pt2.x) {\n          objetsEnonce.push(latexParCoordonnees('(d_2)', pt2.x + 2.5, pt2.y, context.isAmc ? 'black' : 'red', 20, 10, '', 12))\n          objetsCorrection.push(latexParCoordonnees('(d_2)', pt2.x + 2.5, pt2.y, context.isAmc ? 'black' : 'red', 20, 10, '', 12))\n        } else {\n          objetsEnonce.push(latexParCoordonnees('(d_2)', pt2.x + 3.5, pt2.y + 1, context.isAmc ? 'black' : 'red', 20, 10, '', 12))\n          objetsCorrection.push(latexParCoordonnees('(d_2)', pt2.x + 3.5, pt2.y + 1, context.isAmc ? 'black' : 'red', 20, 10, '', 12))\n        }\n\n        pt1 = pointIntersectionDD(mediatrice3, droiteVerticaleParPoint(point(context.fenetreMathalea2d[2], context.fenetreMathalea2d[3])))\n        objetsEnonce.push(latexParCoordonnees('(d_3)', pt1.x - 2, pt1.y + 1.5, context.isAmc ? 'black' : 'blue', 20, 10, '', 12))\n        objetsCorrection.push(latexParCoordonnees('(d_3)', pt1.x - 2, pt1.y + 1.5, context.isAmc ? 'black' : 'blue', 20, 10, '', 12))\n        objetsCorrection.push(segCorr11, segCorr12, segCorr21, segCorr22, segCorr31, segCorr32)\n        objetsCorrection.push(codageSegments('OO', context.isAmc ? 'black' : 'green', segCorr11, segCorr12))\n        objetsCorrection.push(codageSegments('XX', context.isAmc ? 'black' : 'red', segCorr21, segCorr22))\n        objetsCorrection.push(codageSegments('|||', context.isAmc ? 'black' : 'blue', segCorr31, segCorr32))\n        consigneAMC = mathalea2d({\n          xmin: Xmin,\n          xmax: Xmax,\n          ymin: Ymin,\n          ymax: Ymax,\n          pixelsParCm: 15,\n          scale: 0.3,\n          optionsTikz: ['every node/.style={scale=0.6}'],\n          mainlevee: false\n        }, objetsEnonce\n        )\n        texte += consigneAMC\n        quad1 = translation(quad[num1], vecteur(0, 0))\n        quad1.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n        quad1.opaciteDeRemplissage = 0.3\n        quad2 = translation(quad[num2], vecteur(0, 0))\n        quad2.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n        quad2.opaciteDeRemplissage = 0.3\n        quad3 = translation(quad[num3], vecteur(0, 0))\n        quad3.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n        quad3.opaciteDeRemplissage = 0.3\n        objetsCorrection.push(quad[numA], quad[numD], quad[numC], quad1, quad2, quad3)\n        texteCorr += mathalea2d({\n          xmin: Xmin,\n          xmax: Xmax,\n          ymin: Ymin,\n          ymax: Ymax,\n          pixelsParCm: 15,\n          scale: 0.3,\n          optionsTikz: ['every node/.style={scale=0.6}'],\n          mainlevee: false\n        }, objetsCorrection\n        )\n\n        break\n      case 2: // symétrie centrale\n        // First question: a figure in tabfigA, a symmetry with respect to the middle of a [B'C'], logically: the image is in tabfigB and B' is the image of C!\n        indexA = randint(0, nx * ny - 1)\n        numA = tabfigA[indexA][2]\n        indexcentre1 = randint(0, nx * ny - 1, indexA) // indexcentre1 est l'index du bloc de 4 figures A,B,C et D, il sert dans les 4 tableaux.\n\n        // we calculate the coordinates of the middle of [BC] we add to the coordinates of the middle of [BC] those of the vector BB'. (I could have reduced but that would have made the calculation more opaque)\n        xmil1 = (xB + xC) / 2 + tabfigB[indexcentre1][0] - xB\n        ymil1 = (yB + yC) / 2 + tabfigB[indexcentre1][1] - yB\n        punto = imagePointParTransformation(7, [tabfigC[indexA][0], tabfigC[indexA][1]], [xmil1, ymil1])\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigB[j][0], 0.001) && egal(punto[1], tabfigB[j][1], 0.001)) {\n              trouver = true\n              num1 = tabfigB[j][2]\n              xa = tabfigA[indexA][0]\n              ya = tabfigA[indexA][1]\n              centre1 = point(xmil1, ymil1, s0, 'left')\n              quad[numA].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n              quad[numA].opaciteDeRemplissage = 0.6\n              break\n            }\n          }\n          if (trouver === false) {\n            indexA = randint(0, nx * ny - 1)\n            numA = tabfigA[indexA][2]\n            indexcentre1 = randint(0, nx * ny - 1, indexA)\n            xmil1 = (xB + xC) / 2 + tabfigB[indexcentre1][0] - xB\n            ymil1 = (yB + yC) / 2 + tabfigB[indexcentre1][1] - yB\n            punto = imagePointParTransformation(7, [tabfigC[indexA][0], tabfigC[indexA][1]], [xmil1, ymil1])\n          }\n        }\n        texteAMC1 = numAlpha(0) + texteEnCouleurEtGras(`What is the number of the symmetrical figure of the ${numA} figure in the ${s0} center symmetry?`, context.isAmc ? 'black' : 'green') + ajouteChampTexteMathLive(this, 0, 'width25 inline') + '<br>'\n        texte += texteAMC1\n        texteCorr = numAlpha(0) + texteEnCouleurEtGras(` The symmetrical figure of the ${numA} figure in the ${s0} center symmetry has the number ${num1}.<br>`, context.isAmc ? 'black' : 'green')\n        // Second question: a figure in tabfigD, a symmetry with respect to the middle of a [C'D'], the result is a figure in tabfigA and C' is the image of D!\n        indexD = randint(0, nx * ny - 1)\n        numD = tabfigD[indexD][2]\n        indexcentre2 = randint(0, nx * ny - 1, [indexD]) // indexcentre2 est l'index du bloc de 4 figures A,B,C et D, il sert dans les 4 tableaux.\n\n        // we calculate the coordinates of the middle of [DC] we add to the coordinates of the middle of [DC] those of the vector DD'.\n        xmil2 = (xD + xC) / 2 + tabfigD[indexcentre2][0] - xD\n        ymil2 = (yD + yC) / 2 + tabfigD[indexcentre2][1] - yD\n        punto = imagePointParTransformation(7, [tabfigD[indexD][0], tabfigD[indexD][1]], [xmil2, ymil2])\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigC[j][0], 0.001) && egal(punto[1], tabfigC[j][1], 0.001)) {\n              trouver = true\n              num2 = tabfigA[j][2]\n              xb = tabfigA[indexD][0]\n              yb = tabfigA[indexD][1]\n              centre2 = point(xmil2, ymil2, s1, 'left')\n              quad[numD].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n              quad[numD].opaciteDeRemplissage = 0.6\n\n              break\n            }\n          }\n          if (trouver === false) {\n            indexD = randint(0, nx * ny - 1)\n            numD = tabfigD[indexD][2]\n            indexcentre2 = randint(0, nx * ny - 1, [indexD])\n            xmil2 = (xD + xC) / 2 + tabfigD[indexcentre2][0] - xD\n            ymil2 = (yD + yC) / 2 + tabfigD[indexcentre2][1] - yD\n            punto = imagePointParTransformation(7, [tabfigD[indexD][0], tabfigD[indexD][1]], [xmil2, ymil2])\n          }\n        }\n\n        texteAMC2 = numAlpha(1) + texteEnCouleurEtGras(` What is the number of the symmetrical figure of the ${numD} figure in the ${s1} center symmetry?`, context.isAmc ? 'black' : 'red') + ajouteChampTexteMathLive(this, 1, 'width25 inline') + '<br>'\n        texte += '<br>' + texteAMC2\n        texteCorr += numAlpha(1) + texteEnCouleurEtGras(` The symmetrical figure of the ${numD} figure in the ${s1} center symmetry has the number ${num2}.<br>`, context.isAmc ? 'black' : 'red')\n        // third question: a figure in tabfigC, a symmetry with respect to the symmetry of the middle of [A'D'] with respect to the middle of [C'D']... not very clear\n        // the result is a figure in tabfigD and the point (C'+ vector AC) has the image D'!\n        indexC = randint(0, nx * ny - 1)\n        numC = tabfigC[indexC][2]\n        indexcentre3 = randint(0, nx * ny - 1, [indexC]) // indexcentre2 est l'index du bloc de 4 figures A,B,C et D, il sert dans les 4 tableaux.\n\n        // we calculate the coordinates of the middle of the center of symmetry: (C' + D + AC)/2=AC+AD/2 which we translate from CC' so that makes AC' + AD/2\n        xmil3 = xD / 2 + tabfigC[indexcentre3][0]\n        ymil3 = yD / 2 + tabfigC[indexcentre3][1]\n        punto = imagePointParTransformation(7, [tabfigC[indexC][0] + xC, tabfigC[indexC][1] + yC], [xmil3, ymil3]) // c'est le sommet C + AC qui a pour image D.\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigD[j][0], 0.001) && egal(punto[1], tabfigD[j][1], 0.001)) {\n              trouver = true\n              num3 = tabfigD[j][2]\n              xc = tabfigA[indexC][0]\n              yc = tabfigA[indexC][1]\n              centre3 = point(xmil3, ymil3, s2, 'left')\n              quad[numC].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n              quad[numC].opaciteDeRemplissage = 0.6\n              break\n            }\n          }\n          if (trouver === false) {\n            indexC = randint(0, nx * ny - 1)\n            numC = tabfigC[indexC][2]\n            indexcentre3 = randint(0, nx * ny - 1, [indexC])\n            xmil3 = xD / 2 + tabfigC[indexcentre3][0]\n            ymil3 = yD / 2 + tabfigC[indexcentre3][1]\n            punto = imagePointParTransformation(7, [tabfigC[indexC][0] + xC, tabfigC[indexC][1] + yC], [xmil3, ymil3])\n          }\n        }\n        texteAMC3 = numAlpha(2) + texteEnCouleurEtGras(` What is the number of the symmetrical figure of the ${numC} figure in the ${s2} center symmetry?`, context.isAmc ? 'black' : 'blue') + ajouteChampTexteMathLive(this, 2, 'width25 inline') + '<br>'\n        texte += '<br>' + texteAMC3\n        texteCorr += numAlpha(2) + texteEnCouleurEtGras(` The symmetrical figure of the ${numC} figure in the ${s2} center symmetry has the number ${num3}.<br>`, context.isAmc ? 'black' : 'blue')\n        labelCentre1 = tracePoint(centre1, 'red')\n        labelCentre1.epaisseur = 2\n        labelCentre1.taille = 2\n        labelCentre2 = tracePoint(centre2, 'red')\n        labelCentre2.epaisseur = 2\n        labelCentre2.taille = 2\n        labelCentre3 = tracePoint(centre3, 'red')\n        labelCentre3.epaisseur = 2\n        labelCentre3.taille = 2\n\n        objetsEnonce.push(labelCentre1, labelCentre2, labelCentre3, labelPoint(centre1, 'red'), labelPoint(centre2, 'red'), labelPoint(centre3, 'red'))\n        objetsCorrection.push(labelCentre1, labelCentre2, labelCentre3, labelPoint(centre1, 'red'), labelPoint(centre2, 'red'), labelPoint(centre3, 'red')\n          , rotationAnimee(quad[numA], centre1, 180, `id=\"anim${numeroExercice}A\" hard=\"2s\" repeatcount=\"1\"`), rotationAnimee(quad[numD], centre2, 180, `id=\"anim${numeroExercice}B\" dur=\"2s\" repeatcount=\"1\"`), rotationAnimee(quad[numC], centre3, 180, `id=\"anim${numeroExercice}C\" dur=\"2s\" repeatcount=\"1\"`))\n\n        consigneAMC = mathalea2d({\n          xmin: Xmin,\n          xmax: Xmax,\n          ymin: Ymin,\n          ymax: Ymax,\n          pixelsParCm: 15,\n          scale: 0.3,\n          optionsTikz: ['every node/.style={scale=0.6}'],\n          mainlevee: false\n        }, objetsEnonce\n        )\n        texte += consigneAMC\n        quad1 = translation(quad[num1], vecteur(0, 0))\n        quad1.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n        quad1.opaciteDeRemplissage = 0.3\n        quad2 = translation(quad[num2], vecteur(0, 0))\n        quad2.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n        quad2.opaciteDeRemplissage = 0.3\n        quad3 = translation(quad[num3], vecteur(0, 0))\n        quad3.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n        quad3.opaciteDeRemplissage = 0.3\n        arc1 = arc(point(tabfigA[indexA][0], tabfigA[indexA][1]), centre1, 180)\n        rayon11 = segment(point(tabfigA[indexA][0], tabfigA[indexA][1]), centre1)\n        rayon12 = rotation(rayon11, centre1, 180)\n        rayon11.pointilles = 2\n        rayon12.pointilles = 2\n        arc1.pointilles = 2\n        arc2 = arc(point(tabfigD[indexD][0], tabfigD[indexD][1]), centre2, 180)\n        rayon21 = segment(point(tabfigD[indexD][0], tabfigD[indexD][1]), centre2)\n        rayon22 = rotation(rayon21, centre2, 180)\n        rayon21.pointilles = 2\n        rayon22.pointilles = 2\n        arc2.pointilles = 2\n        arc3 = arc(point(tabfigC[indexC][0], tabfigC[indexC][1]), centre3, 180)\n        rayon31 = segment(point(tabfigC[indexC][0], tabfigC[indexC][1]), centre3)\n        rayon32 = rotation(rayon31, centre3, 180)\n        rayon31.pointilles = 2\n        rayon32.pointilles = 2\n        arc3.pointilles = 2\n        objetsCorrection.push(quad1, quad2, quad3, arc1, arc2, arc3, rayon11, rayon12, rayon21, rayon22, rayon31, rayon32)\n        texteCorr += mathalea2d({\n          xmin: Xmin,\n          xmax: Xmax,\n          ymin: Ymin,\n          ymax: Ymax,\n          pixelsParCm: 15,\n          scale: 0.3,\n          optionsTikz: ['every node/.style={scale=0.6}'],\n          mainlevee: false\n        }, objetsCorrection\n        )\n\n        break\n\n      case 3: // translations\n\n        // First question: a figure in tabfigA, the image in tabfigA...\n        // We choose two type B figures to define the translation vector.\n        indexA = randint(0, nx * ny - 1)\n        numA = tabfigA[indexA][2]\n        iB1 = randint(0, nx * ny - 1)\n        iB2 = randint(0, nx * ny - 1, [iB1])\n        xV1 = tabfigB[iB2][0].differenceFraction(tabfigB[iB1][0])\n        yV1 = tabfigB[iB2][1].differenceFraction(tabfigB[iB1][1])\n        punto = imagePointParTransformation(8, [tabfigA[indexA][0], tabfigA[indexA][1]], [0, 0], [xV1, yV1])\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigA[j][0], 0.001) && egal(punto[1], tabfigA[j][1], 0.001)) {\n              trouver = true\n              num1 = tabfigA[j][2]\n              xa = tabfigA[indexA][0]\n              ya = tabfigA[indexA][1]\n              origine1 = point(tabfigB[iB1][0], tabfigB[iB1][1])\n              vector1 = vecteur(origine1, point(tabfigB[iB2][0], tabfigB[iB2][1]))\n              vecteur1 = vector1.representant(origine1)\n              vecteur1.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n              vecteur1.epaisseur = 2\n              vecteur1.pointilles = 2\n              quad[numA].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n              quad[numA].opaciteDeRemplissage = 0.6\n              break\n            }\n          }\n          if (trouver === false) {\n            indexA = randint(0, nx * ny - 1)\n            numA = tabfigA[indexA][2]\n            iB1 = randint(0, nx * ny - 1)\n            iB2 = randint(0, nx * ny - 1, [iB1])\n            xV1 = tabfigB[iB2][0] - tabfigB[iB1][0]\n            yV1 = tabfigB[iB2][1] - tabfigB[iB1][1]\n            punto = imagePointParTransformation(8, [tabfigA[indexA][0], tabfigA[indexA][1]], [0, 0], [xV1, yV1])\n          }\n        }\n        texteAMC1 = numAlpha(0) + texteEnCouleurEtGras(` In the translation that transforms the ${tabfigB[iB1][2]} figure into the ${tabfigB[iB2][2]} figure, what is the number of the image of the ${numA} figure?`, context.isAmc ? 'black' : 'green') + ajouteChampTexteMathLive(this, 0, 'width25 inline') + '<br>'\n        texte += texteAMC1\n        texteCorr = numAlpha(0) + texteEnCouleurEtGras(` The image figure of the ${numA} figure in the translation which transforms the ${tabfigB[iB1][2]} figure into the ${tabfigB[iB2][2]} figure bears the number ${num1}.<br>`, context.isAmc ? 'black' : 'green')\n        // Second question: a figure in tabfigD, the image in tabfigB...\n        // We choose a figure C and a figure A to define the translation vector.\n        indexD = randint(0, nx * ny - 1)\n        numD = tabfigD[indexD][2]\n        iC1 = randint(0, nx * ny - 1)\n        iA1 = randint(0, nx * ny - 1, [iC1])\n        xV2 = tabfigA[iA1][0] - tabfigC[iC1][0]\n        yV2 = tabfigA[iA1][1] - tabfigC[iC1][1]\n        punto = imagePointParTransformation(8, [tabfigD[indexD][0], tabfigD[indexD][1]], [0, 0], [xV2, yV2])\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigB[j][0], 0.001) && egal(punto[1], tabfigB[j][1], 0.001)) {\n              trouver = true\n              num2 = tabfigB[j][2]\n              xb = tabfigD[indexD][0]\n              yb = tabfigD[indexD][1]\n              origine2 = point(tabfigC[iC1][0], tabfigC[iC1][1])\n              vector2 = vecteur(origine2, point(tabfigA[iA1][0], tabfigA[iA1][1]))\n              vecteur2 = vector2.representant(origine2)\n              vecteur2.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n              vecteur2.epaisseur = 2\n              vecteur2.pointilles = 2\n              quad[numD].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n              quad[numD].opaciteDeRemplissage = 0.6\n              break\n            }\n          }\n          if (trouver === false) {\n            indexD = randint(0, nx * ny - 1)\n            numD = tabfigD[indexD][2]\n            iC1 = randint(0, nx * ny - 1)\n            iA1 = randint(0, nx * ny - 1, [iC1])\n            xV2 = tabfigA[iA1][0] - tabfigC[iC1][0]\n            yV2 = tabfigA[iA1][1] - tabfigC[iC1][1]\n            punto = imagePointParTransformation(8, [tabfigD[indexD][0], tabfigD[indexD][1]], [0, 0], [xV2, yV2])\n          }\n        }\n        texteAMC2 = numAlpha(1) + texteEnCouleurEtGras(` In the translation that transforms the ${tabfigC[iC1][2]} figure into the ${tabfigA[iA1][2]} figure, what is the number of the image of the ${numD} figure?`, context.isAmc ? 'black' : 'red') + ajouteChampTexteMathLive(this, 1, 'width25 inline') + '<br>'\n        texte += '<br>' + texteAMC2\n        texteCorr += numAlpha(1) + texteEnCouleurEtGras(` The image figure of the ${numD} figure in the translation which transforms the ${tabfigC[iC1][2]} figure into the ${tabfigA[iA1][2]} figure bears the number ${num2}.<br>`, context.isAmc ? 'black' : 'red')\n\n        // third question: a figure in tabfigC, the image in tabfigA...\n        // We choose a figure D and a figure B to define the translation vector.\n        indexC = randint(0, nx * ny - 1)\n        numC = tabfigC[indexC][2]\n        iD1 = randint(0, nx * ny - 1)\n        iB3 = randint(0, nx * ny - 1, [iD1])\n        xV3 = tabfigA[iB3][0] - tabfigC[iD1][0]\n        yV3 = tabfigA[iB3][1] - tabfigC[iD1][1]\n        punto = imagePointParTransformation(8, [tabfigC[indexC][0], tabfigC[indexC][1]], [0, 0], [xV3, yV3])\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigA[j][0], 0.001) && egal(punto[1], tabfigA[j][1], 0.001)) {\n              trouver = true\n              num3 = tabfigA[j][2]\n              xc = tabfigC[indexC][0]\n              yc = tabfigC[indexC][1]\n              origine3 = point(tabfigC[iD1][0], tabfigC[iD1][1])\n              vector3 = vecteur(origine3, point(tabfigA[iB3][0], tabfigA[iB3][1]))\n              vecteur3 = vector3.representant(origine3)\n              vecteur3.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n              vecteur3.epaisseur = 2\n              vecteur3.pointilles = 2\n              quad[numC].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n              quad[numC].opaciteDeRemplissage = 0.6\n              break\n            }\n          }\n          if (trouver === false) {\n            indexC = randint(0, nx * ny - 1)\n            numC = tabfigC[indexC][2]\n            iD1 = randint(0, nx * ny - 1)\n            iB3 = randint(0, nx * ny - 1, [iD1])\n            xV3 = tabfigA[iB3][0] - tabfigC[iD1][0]\n            yV3 = tabfigA[iB3][1] - tabfigC[iD1][1]\n            punto = imagePointParTransformation(8, [tabfigC[indexC][0], tabfigC[indexC][1]], [0, 0], [xV3, yV3])\n          }\n        }\n        texteAMC3 = numAlpha(2) + texteEnCouleurEtGras(` In the translation that transforms the ${tabfigC[iD1][2]} figure into the ${tabfigA[iB3][2]} figure, what is the number of the image of the ${numC} figure?`, context.isAmc ? 'black' : 'blue') + ajouteChampTexteMathLive(this, 2, 'width25 inline') + '<br>'\n        texte += '<br>' + texteAMC3\n        texteCorr += numAlpha(2) + texteEnCouleurEtGras(` The image figure of the ${numC} figure in the translation which transforms the ${tabfigC[iD1][2]} figure into the ${tabfigA[iB3][2]} figure bears the number ${num3}.<br>`, context.isAmc ? 'black' : 'blue')\n\n        objetsEnonce.push(vecteur1, vecteur2, vecteur3)\n        objetsCorrection.push(vecteur1, vecteur2, vecteur3\n          , translationAnimee(quad[numA], vector1, `id=\"anim${numeroExercice}A\" dur=\"2s\" repeatcount=\"1\"`), translationAnimee(quad[numD], vector2, `id=\"anim${numeroExercice}B\" dur=\"2s\" repeatcount=\"1\"`), translationAnimee(quad[numC], vector3, `id=\"anim${numeroExercice}C\" dur=\"2s\" repeatcount=\"1\"`))\n\n        consigneAMC = mathalea2d({\n          xmin: Xmin,\n          xmax: Xmax,\n          ymin: Ymin,\n          ymax: Ymax,\n          pixelsParCm: 15,\n          scale: 0.3,\n          optionsTikz: ['every node/.style={scale=0.6}'],\n          mainlevee: false\n        }, objetsEnonce\n        )\n        texte += consigneAMC\n        quad1 = translation(quad[num1], vecteur(0, 0))\n        quad1.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n        quad1.opaciteDeRemplissage = 0.3\n        quad2 = translation(quad[num2], vecteur(0, 0))\n        quad2.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n        quad2.opaciteDeRemplissage = 0.3\n        quad3 = translation(quad[num3], vecteur(0, 0))\n        quad3.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n        quad3.opaciteDeRemplissage = 0.3\n        rayon11 = vector1.representant(point(xa, ya))\n        rayon11.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n        rayon11.epaisseur = 2\n        rayon21 = vector2.representant(point(xb, yb))\n        rayon21.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n        rayon21.epaisseur = 2\n        rayon31 = vector3.representant(point(xc, yc))\n        rayon31.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n        rayon31.epaisseur = 2\n        objetsCorrection.push(quad1, quad2, quad3, rayon11, rayon21, rayon31)\n        texteCorr += mathalea2d({\n          xmin: Xmin,\n          xmax: Xmax,\n          ymin: Ymin,\n          ymax: Ymax,\n          pixelsParCm: 15,\n          scale: 0.3,\n          optionsTikz: ['every node/.style={scale=0.6}'],\n          mainlevee: false\n        }, objetsCorrection\n        )\n\n        break\n\n      case 4: // rotations\n\n        // first question: center A, rotation of 90° counterclockwise, a figure of tabfigA gives a figure of tabfigD, point B gives point D.\n        indexA = randint(0, nx * ny - 1)\n        numA = tabfigA[indexA][2]\n        indexcentre1 = randint(0, nx * ny - 1, [indexA])\n        xmil1 = tabfigA[indexcentre1][0]\n        ymil1 = tabfigA[indexcentre1][1]\n        punto = imagePointParTransformation(6, [tabfigB[indexA][0], tabfigB[indexA][1]], [xmil1, ymil1]) // le repère est direct, donc le sens de rotation est inversé...\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigD[j][0], 0.001) && egal(punto[1], tabfigD[j][1], 0.001)) {\n              trouver = true\n              num1 = tabfigD[j][2]\n              xa = tabfigA[indexA][0]\n              ya = tabfigA[indexA][1]\n              centre1 = point(xmil1, ymil1, s0, 'above left')\n              quad[numA].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n              quad[numA].opaciteDeRemplissage = 0.6\n              break\n            }\n          }\n          if (trouver === false) {\n            indexA = randint(0, nx * ny - 1)\n            numA = tabfigA[indexA][2]\n            indexcentre1 = randint(0, nx * ny - 1, [indexA])\n            xmil1 = tabfigA[indexcentre1][0]\n            ymil1 = tabfigA[indexcentre1][1]\n            punto = imagePointParTransformation(6, [tabfigB[indexA][0], tabfigB[indexA][1]], [xmil1, ymil1]) // le repère est direct, donc le sens de rotation est inversé...\n          }\n        }\n        texteAMC1 = numAlpha(0) + ' What is the number of the figure image of the figure ' + texteEnCouleurEtGras(`${numA}`, context.isAmc ? 'black' : 'green') + ' in center rotation ' + texteEnCouleurEtGras(`${s0}`, context.isAmc ? 'black' : 'green') + ' and angle 90° clockwise?' + ajouteChampTexteMathLive(this, 0, 'width25 inline') + '<br>'\n        texte += texteAMC1\n        texteCorr += numAlpha(0) + ' The figure image of the figure ' + texteEnCouleurEtGras(`${numA}`, context.isAmc ? 'black' : 'green') + ' in center rotation ' + texteEnCouleurEtGras(`${s0}`, context.isAmc ? 'black' : 'green') + ' and angle 90° clockwise bears the number ' + texteEnCouleurEtGras(`${num1}`, '#f15929') + '.<br>'\n\n        // second question: center B, rotation 90° clockwise, a figure of tabfigD gives a figure of tabfigC\n        indexD = randint(0, nx * ny - 1)\n        numD = tabfigD[indexD][2]\n        indexcentre2 = randint(0, nx * ny - 1, [indexD])\n        xmil2 = tabfigB[indexcentre2][0]\n        ymil2 = tabfigB[indexcentre2][1]\n        punto = imagePointParTransformation(5, [tabfigD[indexD][0], tabfigD[indexD][1]], [xmil2, ymil2]) // le repère est direct, donc le sens de rotation est inversé...\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], 4 + tabfigC[j][0], 0.001) && egal(punto[1], tabfigC[j][1], 0.001)) {\n              trouver = true\n              num2 = tabfigC[j][2]\n              xb = tabfigA[indexD][0]\n              yb = tabfigA[indexD][1]\n              centre2 = point(xmil2, ymil2, s1, 'above left')\n              quad[numD].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n              quad[numD].opaciteDeRemplissage = 0.6\n              break\n            }\n          }\n          if (trouver === false) {\n            indexD = randint(0, nx * ny - 1)\n            numD = tabfigD[indexD][2]\n            indexcentre2 = randint(0, nx * ny - 1, [indexD])\n            xmil2 = tabfigB[indexcentre2][0]\n            ymil2 = tabfigB[indexcentre2][1]\n            punto = imagePointParTransformation(5, [tabfigD[indexD][0], tabfigD[indexD][1]], [xmil2, ymil2]) // le repère est direct, donc le sens de rotation est inversé...\n          }\n        }\n        texteAMC2 = numAlpha(1) + ' What is the number of the figure image of the figure ' + texteEnCouleurEtGras(`${numD}`, context.isAmc ? 'black' : 'red') + ' in center rotation ' + texteEnCouleurEtGras(`${s1}`, context.isAmc ? 'black' : 'red') + ' and angle 90° counterclockwise?' + ajouteChampTexteMathLive(this, 1, 'width25 inline') + '<br>'\n        texte += '<br>' + texteAMC2\n        texteCorr += '<br>' + numAlpha(1) + ' The figure image of the figure ' + texteEnCouleurEtGras(`${numD}`, context.isAmc ? 'black' : 'red') + ' in center rotation ' + texteEnCouleurEtGras(`${s1}`, context.isAmc ? 'black' : 'red') + ' and angle 90° counterclockwise bears the number ' + texteEnCouleurEtGras(`${num2}`, '#f15929') + '.<br>'\n\n        // third question: center B, rotation 90° counterclockwise, a figure of tabfigC gives a figure of tabfigD\n        indexC = randint(0, nx * ny - 1)\n        numC = tabfigC[indexC][2]\n        indexcentre3 = randint(0, nx * ny - 1, [indexC])\n        xmil3 = tabfigB[indexcentre3][0]\n        ymil3 = tabfigB[indexcentre3][1]\n        punto = imagePointParTransformation(6, [tabfigC[indexC][0], tabfigC[indexC][1]], [xmil3, ymil3]) // le repère est direct, donc le sens de rotation est inversé...\n        trouver = false\n        while (trouver === false) {\n          for (let j = 0; j < nx * ny; j++) {\n            if (egal(punto[0], tabfigD[j][0], 0.001) && egal(punto[1], 4 + tabfigD[j][1], 0.001)) {\n              trouver = true\n              num3 = tabfigD[j][2]\n              xc = tabfigA[indexC][0]\n              yc = tabfigA[indexC][1]\n              centre3 = point(xmil3, ymil3, s2, 'above left')\n              quad[numC].couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n              quad[numC].opaciteDeRemplissage = 0.6\n              break\n            }\n          }\n          if (trouver === false) {\n            indexC = randint(0, nx * ny - 1)\n            numC = tabfigC[indexC][2]\n            indexcentre3 = randint(0, nx * ny - 1, [indexC])\n            xmil3 = tabfigB[indexcentre3][0]\n            ymil3 = tabfigB[indexcentre3][1]\n            punto = imagePointParTransformation(6, [tabfigC[indexC][0], tabfigC[indexC][1]], [xmil3, ymil3]) // le repère est direct, donc le sens de rotation est inversé...\n          }\n        }\n        texteAMC3 = numAlpha(2) + ' What is the number of the figure image of the figure ' + texteEnCouleurEtGras(`${numC}`, context.isAmc ? 'black' : 'blue') + ' in center rotation ' + texteEnCouleurEtGras(`${s2}`, context.isAmc ? 'black' : 'blue') + ' and angle 90° clockwise?' + ajouteChampTexteMathLive(this, 2, 'width25 inline') + '<br>'\n        texte += '<br>' + texteAMC3\n        texteCorr += '<br>' + numAlpha(2) + ' The figure image of the figure ' + texteEnCouleurEtGras(`${numC}`, context.isAmc ? 'black' : 'blue') + ' in center rotation ' + texteEnCouleurEtGras(`${s2}`, context.isAmc ? 'black' : 'blue') + ' and angle 90° clockwise bears the number ' + texteEnCouleurEtGras(`${num3}`, '#f15929') + '.<br>'\n\n        trace = tracePoint(centre1, context.isAmc ? 'black' : 'green')\n        label = labelPoint(centre1, context.isAmc ? 'black' : 'green')\n        trace.epaisseur = 2\n        trace.taille = 4\n        objetsEnonce.push(trace, label)\n        objetsCorrection.push(trace, label)\n        trace = tracePoint(centre2, context.isAmc ? 'black' : 'red')\n        label = labelPoint(centre2, context.isAmc ? 'black' : 'red')\n        trace.epaisseur = 2\n        trace.taille = 4\n        objetsEnonce.push(trace, label)\n        objetsCorrection.push(trace, label)\n        trace = tracePoint(centre3, context.isAmc ? 'black' : 'blue')\n        label = labelPoint(centre3, context.isAmc ? 'black' : 'blue')\n        trace.epaisseur = 2\n        trace.taille = 4\n        objetsEnonce.push(trace, label)\n        objetsCorrection.push(trace, label)\n        objetsCorrection.push(rotationAnimee(quad[numA], centre1, -90, `id=\"anim${numeroExercice}A\" hard=\"2s\" repeatcount=\"1\"`), rotationAnimee(quad[numD], centre2, 90, `id=\"anim${numeroExercice}B\" dur=\"2s\" repeatcount=\"1\"`), rotationAnimee(quad[numC], centre3, -90, `id=\"anim${numeroExercice}C\" dur=\"2s\" repeatcount=\"1\"`))\n\n        consigneAMC = mathalea2d({\n          xmin: Xmin,\n          xmax: Xmax,\n          ymin: Ymin,\n          ymax: Ymax,\n          pixelsParCm: 15,\n          scale: 0.3,\n          optionsTikz: ['every node/.style={scale=0.6}'],\n          mainlevee: false\n        }, objetsEnonce\n        )\n        texte += consigneAMC\n        quad1 = translation(quad[num1], vecteur(0, 0))\n        quad1.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n        quad1.opaciteDeRemplissage = 0.3\n        quad2 = translation(quad[num2], vecteur(0, 0))\n        quad2.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n        quad2.opaciteDeRemplissage = 0.3\n        quad3 = translation(quad[num3], vecteur(0, 0))\n        quad3.couleurDeRemplissage = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n        quad3.opaciteDeRemplissage = 0.3\n        arc1 = arc(point(tabfigA[indexA][0], tabfigA[indexA][1]), centre1, -90)\n        rayon11 = segment(point(tabfigA[indexA][0], tabfigA[indexA][1]), centre1, context.isAmc ? 'black' : 'green')\n        rayon12 = rotation(rayon11, centre1, -90)\n        rayon11.pointilles = 2\n        rayon12.pointilles = 2\n        rayon12.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n        arc1.pointilles = 2\n        arc1.epaisseur = 2\n        arc1.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'green')\n        arc2 = arc(point(tabfigD[indexD][0], tabfigD[indexD][1]), centre2, 90)\n        rayon21 = segment(point(tabfigD[indexD][0], tabfigD[indexD][1]), centre2, context.isAmc ? 'black' : 'red')\n        rayon22 = rotation(rayon21, centre2, 90)\n        rayon21.pointilles = 2\n        rayon22.pointilles = 2\n        rayon22.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n        arc2.pointilles = 2\n        arc2.epaisseur = 2\n        arc2.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'red')\n        arc3 = arc(point(tabfigC[indexC][0], tabfigC[indexC][1]), centre3, -90)\n        rayon31 = segment(point(tabfigC[indexC][0], tabfigC[indexC][1]), centre3, context.isAmc ? 'black' : 'blue')\n        rayon32 = rotation(rayon31, centre3, -90)\n        rayon31.pointilles = 2\n        rayon32.pointilles = 2\n        rayon32.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n        arc3.pointilles = 2\n        arc3.epaisseur = 2\n        arc3.color = colorToLatexOrHTML(context.isAmc ? 'black' : 'blue')\n        objetsCorrection.push(quad1, quad2, quad3, arc1, arc2, arc3, rayon11, rayon12, rayon21, rayon22, rayon31, rayon32,\n          codageAngleDroit(point(tabfigA[indexA][0], tabfigA[indexA][1]), centre1, rotation(point(tabfigA[indexA][0], tabfigA[indexA][1]), centre1, -90), context.isAmc ? 'black' : 'green', 1, 1),\n          codageAngleDroit(point(tabfigD[indexD][0], tabfigD[indexD][1]), centre2, rotation(point(tabfigD[indexD][0], tabfigD[indexD][1]), centre2, 90), context.isAmc ? 'black' : 'red', 1, 1),\n          codageAngleDroit(point(tabfigC[indexC][0], tabfigC[indexC][1]), centre3, rotation(point(tabfigC[indexC][0], tabfigC[indexC][1]), centre3, -90), context.isAmc ? 'black' : 'blue', 1, 1),\n          codageSegments('|||', context.isAmc ? 'black' : 'green', rayon11, rayon12), codageSegments('OO', context.isAmc ? 'black' : 'red', rayon21, rayon22), codageSegments('XXX', context.isAmc ? 'black' : 'blue', rayon31, rayon32))\n        texteCorr += mathalea2d(\n          Object.assign({}, fixeBordures(objetsCorrection), {\n            pixelsParCm: 15,\n            scale: 0.3,\n            optionsTikz: ['every node/.style={scale=0.6}'],\n            mainlevee: false\n          })\n          , objetsCorrection\n        )\n\n        break\n    }\n    setReponse(this, 0, num1)\n    setReponse(this, 1, num2)\n    setReponse(this, 2, num3)\n    if (context.isHtml) {\n      texteCorr += '<br>'\n      texteCorr += `<button class=\"btn ui labeled icon button\" style=\"margin:10px\" onclick=\"document.getElementById('anim${numeroExercice}A').beginElement()\"><i class=\"redo circle icon\"></i>Relaunch green animation</button>`\n      texteCorr += `<button class=\"btn ui labeled icon button\" style=\"margin:10px\" onclick=\"document.getElementById('anim${numeroExercice}B').beginElement()\"><i class=\"redo circle icon\"></i>Relaunch red animation</button>`\n      texteCorr += `<button class=\"btn ui labeled icon button\" style=\"margin:10px\" onclick=\"document.getElementById('anim${numeroExercice}C').beginElement()\"><i class=\"redo circle icon\"></i>Relaunch blue animation</button>`\n    }\n    this.listeQuestions.push(texte)\n    this.listeCorrections.push(texteCorr)\n    listeQuestionsToContenuSansNumero(this)\n    if (context.isAmc) {\n      this.autoCorrection[0] = {\n        enonce: consigneAMC,\n        options: { multicols: true },\n        propositions: [\n          {\n            type: 'AMCNum',\n            propositions: [{\n              texte: texteCorr,\n              statut: '',\n              reponse: {\n                texte: texteAMC1,\n                valeur: num1,\n                param: {\n                  digits: 2,\n                  decimals: 0,\n                  signe: false,\n                  approx: 0\n                }\n              }\n            }]\n          },\n          {\n            type: 'AMCNum',\n            propositions: [{\n              texte: '',\n              statut: '',\n              reponse: {\n                texte: texteAMC2,\n                valeur: num2,\n                param: {\n                  digits: 2,\n                  decimals: 0,\n                  signe: false,\n                  approx: 0\n                }\n              }\n            }]\n          },\n          {\n            type: 'AMCNum',\n            propositions: [{\n              texte: '',\n              statut: '',\n              reponse: {\n                texte: texteAMC3,\n                valeur: num3,\n                param: {\n                  digits: 2,\n                  decimals: 0,\n                  signe: false,\n                  approx: 0\n                }\n              }\n            }]\n          }]\n      }\n    }\n  }\n  this.besoinFormulaireNumerique = ['Transformations', 4, ' 1: Axial symmetries\\n 2: Central symmetries\\n 3: Translations\\n 4: Rotations\\n 5: 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