File: /home/mmtprep/public_html/mathzen.mmtprep.com/assets/_Transformations-XkjJqMTJ.js.map
{"version":3,"file":"_Transformations-XkjJqMTJ.js","sources":["../../src/exercices/6e/_Transformations.js"],"sourcesContent":["import { codageAngleDroit } from '../../lib/2d/angles.js'\nimport { afficheMesureAngle, codageSegments } from '../../lib/2d/codages.js'\nimport { droiteHorizontaleParPoint, droiteParPointEtPente, droiteVerticaleParPoint } from '../../lib/2d/droites.js'\nimport { milieu, point, pointSurDroite, tracePoint } from '../../lib/2d/points.js'\nimport { segment, vecteur } from '../../lib/2d/segmentsVecteurs.js'\nimport { labelLatexPoint, latexParCoordonnees, texteParPositionEchelle } from '../../lib/2d/textes.js'\nimport { translation } from '../../lib/2d/transformations.js'\nimport {\n choice,\n combinaisonListes,\n compteOccurences,\n enleveElementBis,\n enleveElementNo\n} from '../../lib/outils/arrayOutils'\nimport { miseEnCouleur, miseEnEvidence } from '../../lib/outils/embellissements'\nimport { texFractionReduite } from '../../lib/outils/deprecatedFractions.js'\nimport { arrondi, rangeMinMax } from '../../lib/outils/nombres.js'\nimport { lettreDepuisChiffre, numAlpha } from '../../lib/outils/outilString.js'\nimport { texNombre } from '../../lib/outils/texNombre.js'\nimport { imagePointParTransformation } from '../../modules/imagePointParTransformation.js'\nimport Exercice from '../Exercice.js'\nimport { assombrirOuEclaircir, colorToLatexOrHTML, mathalea2d } from '../../modules/2dGeneralites.js'\nimport { context } from '../../modules/context.js'\nimport { egal, gestionnaireFormulaireTexte, listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.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/**\n * Transformations : trouver un point numéroté par une des transformations du plan. Fonction générale utilisée sur tous les niveaux\n * @author Jean-Claude Lhote\n *\n * Relecture : Novembre 2021 par EE\n */\nexport default function Transformations () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.can = false\n this.consigne = ''\n this.nbQuestions = 1\n this.nbCols = 1\n this.nbColsCorr = 1\n this.sup = 1\n\n this.nouvelleVersion = function () {\n let nbImages\n\n const choixTransformation = gestionnaireFormulaireTexte({\n max: 10,\n defaut: randint(1, 10),\n nbQuestions: 3,\n saisie: this.sup\n })\n\n if (this.can) {\n nbImages = 1\n } else nbImages = 3\n\n const O = point(0, 0, 'O', 'above right')\n const d1 = droiteParPointEtPente(O, 1)\n const d3 = droiteHorizontaleParPoint(O)\n const d2 = droiteParPointEtPente(O, -1)\n const d4 = droiteVerticaleParPoint(O)\n d1.isVisible = true\n d2.isVisible = true\n d3.isVisible = true\n d4.isVisible = true\n d1.epaisseur = 2\n d2.epaisseur = 2\n d3.epaisseur = 2\n d4.epaisseur = 2\n d1.opacite = 0.5\n d2.opacite = 0.5\n d3.opacite = 0.5\n d4.opacite = 0.5\n const couleurs = ['brown', 'green', 'blue']\n this.listeQuestions = []\n this.listeCorrections = [] // Liste de questions corrigées\n const xO = 4\n const yO = 4\n const xuPossibles = combinaisonListes(rangeMinMax(-3, 3), 1)\n const yuPossibles = combinaisonListes(rangeMinMax(-3, 3), 1)\n\n for (let ee = 0, texte, texteCorr, xu, yu, pointMLettre, pointM, pointN, numPointN, croix, aEviter, mauvaisAntecedents, longueurBoucle, objetsEnonce, objetsCorrection, cpt = 0; ee < this.nbQuestions && cpt < 50;) {\n texte = ''\n texteCorr = ''\n objetsEnonce = []\n objetsCorrection = []\n const antecedents = [0, 0, 0]\n const images = [0, 0, 0]\n const k = [1, 1, 1]\n const punto = [[]]\n const n = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]\n const M = []\n const N = []\n // Below, we avoid the point $O$ as a point and as a point name.\n const nomPointsTranslationDejaUtilises = [15]\n const pointsDejaUtilises = [44]\n aEviter = [44]\n mauvaisAntecedents = []\n for (let i = 0; i < 10; i++) {\n for (let j = 0; j < 10; j++) {\n croix = tracePoint(point(j - 4, i - 4), 'gray')\n croix.taille = 2\n croix.style = 'x'\n croix.opacite = 1\n objetsEnonce.push(croix)\n objetsCorrection.push(tracePoint(point(j - 4, i - 4), assombrirOuEclaircir('gray', 50)))\n objetsEnonce.push(texteParPositionEchelle(Number(j + 10 * i).toString(), j - 4.2, i - 4.2, 'medium', 'black', 0.8, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(Number(j + 10 * i).toString(), j - 4.2, i - 4.2, 'medium', assombrirOuEclaircir('gray', 50), 0.8, 'middle', false, 0.8))\n }\n }\n let puntoReseau // k : rapports d'homothéties, (xO,yO) point de rencontre des droites et centre, les composantes du vecteur de translation : (xu,yu)\n for (let j = 0; j < nbImages; j++) {\n xu = xuPossibles[j]\n if (xu === 0) {\n if (yuPossibles[j] === 0) {\n enleveElementNo(yuPossibles, j)\n }\n }\n yu = yuPossibles[j]\n if (choixTransformation[j] === 10) {\n k[j] = choice([2, 3, 4]) * randint(-1, 1, [0]) // rapport d'homothétie < 1 ( 0.5 ou 0.25 )\n } else if (choixTransformation[j] === 9) {\n k[j] = choice([1, 1.5, 2, 2.5, 3, 4, 5]) * randint(-1, 1, [0]) // rapport d'homothétie >=1 (1,2 ou 3)\n }\n mauvaisAntecedents = []\n antecedents[j] = randint(0, 99, pointsDejaUtilises)\n punto[j] = imagePointParTransformation(\n choixTransformation[j],\n [antecedents[j] % 10, Math.floor(antecedents[j] / 10)],\n [xO, yO],\n [xu, yu],\n k[j]\n )\n images[j] = punto[j][0] + punto[j][1] * 10\n // Limitation of invariant points\n if (choixTransformation[j] === 1 && images[j] % 11 === 0) {\n punto[j][0] = -1\n } // Point impossible sur (d1) pour sa symétrie\n if (choixTransformation[j] === 3 && Math.floor(images[j] / 10 === 4)) {\n punto[j][0] = -1\n } // Point impossible sur (d3) pour sa symétrie\n if (choixTransformation[j] === 4 && images[j] % 10 === 4) {\n punto[j][0] = -1\n } // Point impossible sur (d4) pour sa symétrie\n\n // to avoid points outside the nails in scale with ratio 1/k\n puntoReseau = egal(punto[j][0], Math.floor(punto[j][0]), 0.001) &&\n egal(punto[j][1], Math.floor(punto[j][1]), 0.001)\n // We check that the image is indeed a point in the network, otherwise, we change.\n mauvaisAntecedents = combinaisonListes(pointsDejaUtilises, 1)\n while (punto[j][0] < 0 ||\n punto[j][0] > 9 ||\n punto[j][1] < 0 ||\n punto[j][1] > 9 ||\n puntoReseau === false) {\n mauvaisAntecedents.push(antecedents[j])\n antecedents[j] = randint(0, 99, mauvaisAntecedents)\n punto[j] = imagePointParTransformation(\n choixTransformation[j],\n [antecedents[j] % 10, Math.floor(antecedents[j] / 10)],\n [xO, yO],\n [xu, yu],\n k[j]\n )\n images[j] = arrondi(punto[j][0] + punto[j][1] * 10, 0)\n // Limitation of invariant points\n if (choixTransformation[j] === 1 && images[j] % 11 === 0) {\n punto[j][0] = -1\n } // Point impossible sur (d1) pour sa symétrie\n if (choixTransformation[j] === 3 && Math.floor(images[j] / 10 === 4)) {\n punto[j][0] = -1\n } // Point impossible sur (d3) pour sa symétrie\n if (choixTransformation[j] === 4 && images[j] % 10 === 4) {\n punto[j][0] = -1\n } // Point impossible sur (d4) pour sa symétrie\n\n // to avoid points outside the nails in scale with ratio 1/k\n if (egal(punto[j][0], Math.floor(punto[j][0]), 0.001) &&\n egal(punto[j][1], Math.floor(punto[j][1]), 0.001)) {\n puntoReseau = true\n } else {\n puntoReseau = false\n }\n }\n N[j] = point(arrondi(punto[j][0] - 4, 0), arrondi(punto[j][1] - 4, 0), 'above left')\n M[j] = point(antecedents[j] % 10 - 4, Math.floor(antecedents[j] / 10 - 4), 'above left')\n pointsDejaUtilises.push(antecedents[j])\n pointsDejaUtilises.push(arrondi(punto[j][0] + 10 * punto[j][1], 0))\n }\n // n[i] is an array containing -1 for the transformation of index i if it is not used, and containing the number of the point concerned if the transformation i is used for this point.\n // I use it to show the correction linked to the point and the transformation.\n for (let j = 0; j < nbImages; j++) {\n n[choixTransformation[j] - 1] = antecedents[j]\n }\n const questionsAMC = [0, 0, 0]\n\n for (let i = 0, labO, labM, labN, traceAnt, traceIm, traceO, traceM, traceN; i < nbImages; i++) {\n xu = xuPossibles[i]\n yu = yuPossibles[i]\n traceAnt = tracePoint(M[i])\n traceIm = tracePoint(N[i])\n traceAnt.epaisseur = 2\n traceAnt.opacite = 1\n traceIm.opacite = 1\n traceIm.epaisseur = 2\n traceIm.color = colorToLatexOrHTML('#f15929')\n traceO = tracePoint(O)\n traceO.epaisseur = 2\n traceO.opacite = 1\n labO = labelLatexPoint({ points: [O], color: 'red', taille: 10 })\n labO.taille = 12\n switch (choixTransformation[i]) {\n case 1:\n d1.color = colorToLatexOrHTML(context.isHtml ? couleurs[i] : 'black')\n questionsAMC[i] = numAlpha(i) +\n ` Give the number of the symmetric of the point $${antecedents[i]}$ with respect to the line $(d_1)$.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the symmetric of the point $${antecedents[i]}$ with respect to the line $${miseEnCouleur('(d_1)', d1.color)}$.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The symmetric of the point $${antecedents[i]}$ with respect to $${miseEnCouleur('(d_1)', d1.color)}$ is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(d1, traceAnt, latexParCoordonnees('(d_1)', 4.8, 4.2, d1.color, 20, 10, '', 12))\n\n objetsCorrection.push(d1, traceAnt, traceIm, latexParCoordonnees('(d_1)', 4.8, 4.2, d1.color, 20, 10, '', 12),\n segment(M[i], N[i], d1.color), codageSegments('O', d1.color, M[i], milieu(M[i], N[i]), milieu(M[i], N[i]), N[i]),\n codageAngleDroit(M[i], milieu(M[i], N[i]), pointSurDroite(d1, 1), d1.color, 0.4, 1))\n objetsCorrection.push(texteParPositionEchelle(Number(punto[i][0] + 10 * punto[i][1]).toString(), punto[i][0] - 4.2, punto[i][1] - 4.2, 'medium', '#f15929', 1, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(antecedents[i].toString(), antecedents[i] % 10 - 4.2, Math.floor(antecedents[i] / 10) - 4.2, 'medium', d1.color, 1, 'middle', false, 0.8))\n break\n\n case 2:\n d2.color = colorToLatexOrHTML(context.isHtml ? couleurs[i] : 'black')\n questionsAMC[i] = numAlpha(i) +\n ` Give the number of the symmetric of the point $${antecedents[i]}$ with respect to the line $(d_2)$.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the symmetric of the point $${antecedents[i]}$ with respect to the line $${miseEnCouleur('(d_2)', d2.color)}$.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The symmetric of the point $${antecedents[i]}$ with respect to $${miseEnCouleur('(d_2)', d2.color)}$ is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(d2, traceAnt, latexParCoordonnees('(d_2)', 4.3, -3.7, d2.color, 20, 10, '', 12))\n objetsCorrection.push(d2, traceAnt, traceIm, latexParCoordonnees('(d_2)', 4.3, -3.7, d2.color, 15, 10, '', 12),\n segment(M[i], N[i], d2.color), codageSegments('||', d2.color, M[i], milieu(M[i], N[i]), milieu(M[i], N[i]), N[i]),\n codageAngleDroit(M[i], milieu(M[i], N[i]), pointSurDroite(d2, 1), d2.color, 0.4, 1))\n objetsCorrection.push(texteParPositionEchelle(Number(punto[i][0] + 10 * punto[i][1]).toString(), punto[i][0] - 4.2, punto[i][1] - 4.2, 'medium', '#f15929', 1, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(antecedents[i].toString(), antecedents[i] % 10 - 4.2, Math.floor(antecedents[i] / 10) - 4.2, 'medium', d2.color, 1, 'middle', false, 0.8))\n break\n\n case 3:\n d3.color = colorToLatexOrHTML(context.isHtml ? couleurs[i] : 'black')\n questionsAMC[i] = numAlpha(i) +\n ` Give the number of the symmetric of the point $${antecedents[i]}$ with respect to the line $(d_3)$.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the symmetric of the point $${antecedents[i]}$ with respect to the line $${miseEnCouleur('(d_3)', d3.color)}$.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The symmetric of the point $${antecedents[i]}$ with respect to $${miseEnCouleur('(d_3)', d3.color)}$ is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(d3, traceAnt, latexParCoordonnees('(d_3)', -4.2, 0.3, d3.color, 20, 10, '', 12))\n objetsCorrection.push(d3, traceAnt, traceIm, latexParCoordonnees('(d_3)', -4.2, 0.3, d3.color, 15, 10, '', 12),\n segment(M[i], N[i], d3.color), codageSegments('///', d3.color, M[i], milieu(M[i], N[i]), milieu(M[i], N[i]), N[i]),\n codageAngleDroit(M[i], milieu(M[i], N[i]), pointSurDroite(d3, 1), d3.color, 0.4, 1))\n objetsCorrection.push(texteParPositionEchelle(Number(punto[i][0] + 10 * punto[i][1]).toString(), punto[i][0] - 4.2, punto[i][1] - 4.2, 'medium', '#f15929', 1, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(antecedents[i].toString(), antecedents[i] % 10 - 4.2, Math.floor(antecedents[i] / 10) - 4.2, 'medium', d3.color, 1, 'middle', false, 0.8))\n break\n\n case 4:\n d4.color = colorToLatexOrHTML(context.isHtml ? couleurs[i] : 'black')\n questionsAMC[i] = numAlpha(i) +\n ` Give the number of the symmetric of the point $${antecedents[i]}$ with respect to the line $(d_4)$.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the symmetric of the point $${antecedents[i]}$ with respect to the line $${miseEnCouleur('(d_4)', d4.color)}$.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The symmetric of the point $${antecedents[i]}$ with respect to $${miseEnCouleur('(d_4)', d4.color)}$ is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(d4, traceAnt, latexParCoordonnees('(d_4)', 0.2, 4.5, d4.color, 15, 10, '', 12))\n objetsCorrection.push(d4, traceAnt, traceIm, latexParCoordonnees('(d_4)', 0.2, 4.5, d4.color, 20, 10, '', 12),\n segment(M[i], N[i], d4.color), codageSegments('OO', d4.color, M[i], milieu(M[i], N[i]), milieu(M[i], N[i]), N[i]),\n codageAngleDroit(M[i], milieu(M[i], N[i]), pointSurDroite(d4, 1), '#f15929', 0.4, 1))\n objetsCorrection.push(texteParPositionEchelle(Number(punto[i][0] + 10 * punto[i][1]).toString(), punto[i][0] - 4.2, punto[i][1] - 4.2, 'medium', '#f15929', 1, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(antecedents[i].toString(), antecedents[i] % 10 - 4.2, Math.floor(antecedents[i] / 10) - 4.2, 'medium', d4.color, 1, 'middle', false, 0.8))\n break\n\n case 5:\n questionsAMC[i] = numAlpha(i) + ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 90° counterclockwise.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 90° counterclockwise.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 90° counterclockwise is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(traceAnt, traceO, labO)\n objetsCorrection.push(traceAnt, traceIm, traceO, labO, segment(M[i], O, couleurs[i]), segment(N[i], O, couleurs[i]), codageSegments('|||', couleurs[i], M[i], O, O, N[i]), afficheMesureAngle(M[i], O, N[i]),\n codageAngleDroit(M[i], O, N[i], couleurs[i], 0.4, 1))\n objetsCorrection.push(texteParPositionEchelle(Number(punto[i][0] + 10 * punto[i][1]).toString(), punto[i][0] - 4.2, punto[i][1] - 4.2, 'medium', '#f15929', 1, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(antecedents[i].toString(), antecedents[i] % 10 - 4.2, Math.floor(antecedents[i] / 10) - 4.2, 'medium', couleurs[i], 1, 'middle', false, 0.8))\n break\n\n case 6:\n questionsAMC[i] = numAlpha(i) + ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 90° clockwise.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 90° clockwise.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 90° clockwise is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(traceAnt, traceO, labO)\n objetsCorrection.push(traceAnt, traceIm, traceO, labO, segment(M[i], O, couleurs[i]), segment(N[i], O, couleurs[i]), codageSegments('////', 'red', M[i], O, O, N[i]), afficheMesureAngle(M[i], O, N[i]),\n codageAngleDroit(M[i], O, N[i], couleurs[i], 0.8, 1))\n objetsCorrection.push(texteParPositionEchelle(Number(punto[i][0] + 10 * punto[i][1]).toString(), punto[i][0] - 4.2, punto[i][1] - 4.2, 'medium', '#f15929', 1, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(antecedents[i].toString(), antecedents[i] % 10 - 4.2, Math.floor(antecedents[i] / 10) - 4.2, 'medium', couleurs[i], 1, 'middle', false, 0.8))\n break\n\n case 7:\n questionsAMC[i] = numAlpha(i) + ` Give the number of the image of the point $${antecedents[i]}$ by the symmetry of center O.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the image of the point $${antecedents[i]}$ by the symmetry of center O.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The image of the point $${antecedents[i]}$ by the symmetry of center $O$ is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(traceAnt, traceO, labO)\n objetsCorrection.push(traceAnt, traceIm, traceO, labO, segment(M[i], O, couleurs[i]), segment(N[i], O, couleurs[i]), codageSegments('OOO', couleurs[i], M[i], O, O, N[i]))\n objetsCorrection.push(texteParPositionEchelle(Number(punto[i][0] + 10 * punto[i][1]).toString(), punto[i][0] - 4.2, punto[i][1] - 4.2, 'medium', '#f15929', 1, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(antecedents[i].toString(), antecedents[i] % 10 - 4.2, Math.floor(antecedents[i] / 10) - 4.2, 'medium', couleurs[i], 1, 'middle', false, 0.8))\n break\n\n case 8:\n pointMLettre = randint(1, 26, nomPointsTranslationDejaUtilises)\n nomPointsTranslationDejaUtilises.push(pointMLettre)\n numPointN = randint(1, 26, nomPointsTranslationDejaUtilises)\n nomPointsTranslationDejaUtilises.push(numPointN)\n questionsAMC[i] = numAlpha(i) + ` Give the number of the image of the point $${antecedents[i]}$ by the translation which transforms ${lettreDepuisChiffre(pointMLettre)} into ${lettreDepuisChiffre(numPointN)}.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the image of the point $${antecedents[i]}$ by the translation which transforms ${lettreDepuisChiffre(pointMLettre)} into ${lettreDepuisChiffre(numPointN)}.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The image of the point $${antecedents[i]}$ by the translation which transforms ${lettreDepuisChiffre(pointMLettre)} into ${lettreDepuisChiffre(numPointN)} is the point $${miseEnEvidence(images[i])}$.<br>`\n aEviter = enleveElementBis(pointsDejaUtilises)\n longueurBoucle = pointsDejaUtilises.length\n for (let kk = 0; kk < longueurBoucle; kk++) {\n aEviter.push(pointsDejaUtilises[kk] - xu - 10 * yu)\n }\n pointM = point(randint(-1, 2, [M[i].x, 0]), randint(-1, 2, [M[i].y, 0]), lettreDepuisChiffre(pointMLettre), 'above right')\n while (compteOccurences(aEviter, 44 + pointM.x + 10 * pointM.y) !== 0) {\n pointM = point(randint(-1, 2, [M[i].x, 0]), randint(-1, 2, [M[i].y, 0]), lettreDepuisChiffre(pointMLettre), 'above right')\n }\n pointN = translation(pointM, vecteur(xu, yu), lettreDepuisChiffre(numPointN), 'above right')\n traceM = tracePoint(pointM)\n traceN = tracePoint(pointN)\n traceM.epaisseur = 1\n traceN.epaisseur = 1\n labM = labelLatexPoint({ points: [pointM], color: couleurs[i], taille: 10 })\n labN = labelLatexPoint({ points: [pointN], color: couleurs[i], taille: 10 })\n labM.taille = 8\n labN.taille = 8\n pointsDejaUtilises.push(44 + pointM.x + 10 * pointM.y)\n pointsDejaUtilises.push(44 + pointN.x + 10 * pointN.y)\n objetsEnonce.push(traceAnt, traceM, traceN, labM, labN)\n objetsCorrection.push(vecteur(M[i], N[i]).representant(M[i], couleurs[i]), vecteur(M[i], N[i]).representant(pointM, couleurs[i]), traceAnt, traceIm, traceM, traceN, labM, labN)\n objetsCorrection.push(texteParPositionEchelle(Number(punto[i][0] + 10 * punto[i][1]).toString(), punto[i][0] - 4.2, punto[i][1] - 4.2, 'medium', '#f15929', 1, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(antecedents[i].toString(), antecedents[i] % 10 - 4.2, Math.floor(antecedents[i] / 10) - 4.2, 'medium', couleurs[i], 1, 'middle', false, 0.8))\n break\n\n case 9:\n questionsAMC[i] = numAlpha(i) + ` Give the number of the image of the point $${antecedents[i]}$ by the homothety of center $O$ and ratio $${texNombre(k[i])}$.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the image of the point $${antecedents[i]}$ by the homothety of center $O$ and ratio $${texNombre(k[i])}$.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The image of the point $${antecedents[i]}$ by the homothety of center $O$ and ratio $${texNombre(k[i])}$ is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(traceAnt, traceO, labO)\n objetsCorrection.push(traceAnt, traceIm, traceO, labO, segment(M[i], O, couleurs[i]), segment(N[i], O, couleurs[i]))\n objetsCorrection.push(texteParPositionEchelle(Number(punto[i][0] + 10 * punto[i][1]).toString(), punto[i][0] - 4.2, punto[i][1] - 4.2, 'medium', '#f15929', 1, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(antecedents[i].toString(), antecedents[i] % 10 - 4.2, Math.floor(antecedents[i] / 10) - 4.2, 'medium', couleurs[i], 1, 'middle', false, 0.8))\n break\n\n case 10:\n questionsAMC[i] = numAlpha(i) +\n ` Donner le numéro de l'image of point $${antecedents[i]}$ by l'homothétie de centre $O$ et de rapport $${texFractionReduite(\n 1,\n k[i]\n )}$.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Donner le numéro de l'image of point $${antecedents[i]}$ by l'homothétie de centre $O$ et de rapport $${texFractionReduite(\n 1,\n k[i]\n )}$.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` L'image of point $${antecedents[i]}$ by l'homothétie de centre $O$ et de rapport $${texFractionReduite(\n 1,\n k[i]\n )}$ est le point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(traceAnt, traceO, labO)\n objetsCorrection.push(traceAnt, traceIm, traceO, labO, segment(M[i], O, couleurs[i]), segment(N[i], O, couleurs[i]))\n objetsCorrection.push(texteParPositionEchelle(Number(punto[i][0] + 10 * punto[i][1]).toString(), punto[i][0] - 4.2, punto[i][1] - 4.2, 'medium', '#f15929', 1, 'middle', false, 0.8))\n objetsCorrection.push(texteParPositionEchelle(antecedents[i].toString(), antecedents[i] % 10 - 4.2, Math.floor(antecedents[i] / 10) - 4.2, 'medium', couleurs[i], 1, 'middle', false, 0.8))\n break\n\n case 11:\n questionsAMC[i] = numAlpha(i) + ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 60° counterclockwise.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 60° counterclockwise.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 60° counterclockwise is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(traceAnt, traceO, labO)\n objetsCorrection.push(traceAnt, traceIm, traceO, labO, segment(M[i], O, 'blue'), segment(N[i], O, 'blue'), codageSegments('||', 'red', M[i], O, O, N[i]), afficheMesureAngle(M[i], O, N[i]))\n break\n\n case 12:\n questionsAMC[i] = numAlpha(i) + ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 60° clockwise.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 60° clockwise.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 60° clockwise is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(traceAnt, traceO, labO)\n objetsCorrection.push(traceAnt, traceIm, traceO, labO, segment(M[i], O, 'blue'), segment(N[i], O, 'blue'), codageSegments('||', 'red', M[i], O, O, N[i]), afficheMesureAngle(M[i], O, N[i]))\n break\n\n case 13:\n questionsAMC[i] = numAlpha(i) + ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 120° counterclockwise.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 120° counterclockwise.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 120° counterclockwise is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(traceAnt, traceO, labO)\n objetsCorrection.push(traceAnt, traceIm, traceO, labO, segment(M[i], O, 'blue'), segment(N[i], O, 'blue'), codageSegments('||', 'red', M[i], O, O, N[i]), afficheMesureAngle(M[i], O, N[i]))\n break\n\n case 14:\n questionsAMC[i] = numAlpha(i) + ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 120° clockwise.`\n texte +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` Give the number of the image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 120° clockwise.<br>`\n texteCorr +=\n (i === 0 ? numAlpha(i) : '<br>' + numAlpha(i)) +\n ` The image of the point $${antecedents[i]}$ by the rotation of center $O$ and angle 120° clockwise is the point $${miseEnEvidence(images[i])}$.<br>`\n objetsEnonce.push(traceAnt, traceO, labO)\n objetsCorrection.push(traceAnt, traceIm, traceO, labO, segment(M[i], O, 'blue'), segment(N[i], O, 'blue'), codageSegments('||', 'red', M[i], O, O, N[i]), afficheMesureAngle(M[i], O, N[i]))\n break\n }\n\n setReponse(this, i, images[i])\n texte += ajouteChampTexteMathLive(this, i, 'width10 inline')\n }\n const graphique = mathalea2d({\n xmin: -4.5,\n ymin: -4.5,\n xmax: 5.8,\n ymax: 5.3,\n pixelsParCm: 40,\n scale: 0.8,\n optionsTikz: ['every node/.style={scale=0.6}'],\n mainlevee: false\n }, objetsEnonce)\n texte += '<br>' + graphique\n texteCorr += '<br>' + mathalea2d({\n xmin: -4.5,\n ymin: -4.5,\n xmax: 5.8,\n ymax: 5.3,\n pixelsParCm: 40,\n scale: 0.8,\n optionsTikz: ['every node/.style={scale=0.6}'],\n mainlevee: false\n }, objetsCorrection)\n\n if (context.isAmc) {\n if (this.can) {\n this.autoCorrection[0] = {\n enonce: texte,\n enonceAGauche: [0.5, 0.5],\n propositions: [\n {\n type: 'AMCNum',\n propositions: [{\n texte: texteCorr,\n statut: '',\n reponse: {\n texte: numAlpha(0),\n valeur: images[0],\n param: {\n digits: 2,\n decimals: 0,\n signe: false,\n approx: 0\n }\n }\n }]\n }]\n\n }\n } else {\n this.autoCorrection[0] = {\n enonce: '<br>\\\\begin{center}' + graphique + '\\\\end{center}',\n enonceAvant: false,\n enonceApresNumQuestion: true,\n options: { barreseparation: true },\n propositions: [\n {\n type: 'AMCNum',\n propositions: [{\n texte: texteCorr,\n statut: '',\n multicolsBegin: true,\n reponse: {\n texte: questionsAMC[0],\n valeur: images[0],\n alignement: 'center',\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: questionsAMC[1],\n valeur: images[1],\n alignement: 'center',\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 multicolsEnd: true,\n reponse: {\n texte: questionsAMC[2],\n valeur: images[2],\n alignement: 'center',\n param: {\n digits: 2,\n decimals: 0,\n signe: false,\n approx: 0\n }\n }\n }]\n }]\n }\n }\n }\n\n if (this.questionJamaisPosee(ee, antecedents)) {\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n if (!context.isHtml) {\n this.canEnonce = this.listeQuestions[0]\n this.correction = this.listeCorrections[0]\n this.canReponseACompleter = ''\n }\n ee++\n }\n cpt++\n }\n listeQuestionsToContenu(this)\n }\n this.besoinFormulaireTexte = [\n 'Choice of transformations',\n 'Choose 3 numbers maximum, separated by hyphens: \\n 1 & 2: Oblique symmetries\\n 3 & 4: Horizontal or vertical symmetries\\n 5 & 6: Rotations of 90°\\n 7: Central symmetry\\n 8: Translation\\n n 9: Homotheties k>1\\n 10: Homotheties k<1'\n 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