{"version":3,"file":"5G13-aFAhdTnN.js","sources":["../../src/exercices/5e/5G13.js"],"sourcesContent":["import { angle } from '../../lib/2d/angles.js'\nimport { afficheLongueurSegment, afficheMesureAngle } from '../../lib/2d/codages.js'\nimport { distancePointDroite, droite, droiteAvecNomLatex, droiteParPointEtParallele, positionLabelDroite } from '../../lib/2d/droites.js'\nimport { point, pointAdistance, tracePoint } from '../../lib/2d/points.js'\nimport { polygoneAvecNom } from '../../lib/2d/polygones.js'\nimport { longueur, segment, vecteur } from '../../lib/2d/segmentsVecteurs.js'\nimport { labelPoint, texteParPoint } from '../../lib/2d/textes.js'\nimport { rotation, symetrieAxiale, translation, translation2Points } from '../../lib/2d/transformations.js'\nimport { triangle2points2longueurs } from '../../lib/2d/triangle.js'\nimport { combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { choisitLettresDifferentes } from '../../lib/outils/aleatoires'\nimport { texNombre } from '../../lib/outils/texNombre.js'\nimport Exercice from '../Exercice.js'\nimport { fixeBordures, mathalea2d } from '../../modules/2dGeneralites.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { context } from '../../modules/context.js'\nexport const titre = 'Use the conservation properties of parallelism, lengths and angles'\n\nexport const dateDePublication = '05/08/2021'\nexport const dateDeModifImportante = '06/03/2023'\n\n/**\n * Compléter le symétrique d'une figure en utilisant les propriétés de conservation de la symétrie et de la translation et en justifiant ses démarches\n * @author Guillaume Valmont\n * Ajout de la translation par Guillaume Valmont le 16/05/2022\n * Les noms des points sont maintenant aléatoires par Guillaume Valmont le 06/03/2023\n*/\nexport const uuid = '07d1a'\nexport const ref = '5G13'\nexport default function ConservationTransformation () {\n  Exercice.call(this)\n  this.consigne = ''\n  this.nbQuestions = 2\n\n  this.besoinFormulaireNumerique = ['Transformations', 4, '1: Axial symmetry\\n2: Central symmetry\\n3: Axial or central symmetry\\n4: Translation'] // Je n'don't add a new mix option, it would be nice to'ajouter la rotation avant.\n  this.besoinFormulaire2Numerique = ['Retained properties', 3, '1: Parallelism\\n2: Lengths and Angles\\n3: Mixture']\n  this.sup = 1\n  this.sup2 = 3\n  this.nbCols = 1\n  this.nbColsCorr = 1\n\n  this.nouvelleVersion = function () {\n    context.fenetreMathalea2d = [-6, -6, 6, 6]\n    this.listeQuestions = []\n    this.listeCorrections = []\n    this.autoCorrection = []\n    this.sup = Number(this.sup)\n    this.sup2 = Number(this.sup2)\n    let typesDeTransformationsDisponibles\n    switch (this.sup) {\n      case 1:\n        typesDeTransformationsDisponibles = ['symmetryAxial']\n        break\n      case 2:\n        typesDeTransformationsDisponibles = ['symmetryCentral']\n        break\n      case 3:\n        typesDeTransformationsDisponibles = ['symmetryAxial', 'symmetryCentral']\n        break\n      case 4:\n        typesDeTransformationsDisponibles = ['translation']\n        break\n    }\n    const listeTypeDeTransformations = combinaisonListes(typesDeTransformationsDisponibles, this.nbQuestions)\n    let typesDeQuestionsDisponibles\n    switch (this.sup2) {\n      case 1:\n        typesDeQuestionsDisponibles = ['parallelism']\n        break\n      case 2:\n        typesDeQuestionsDisponibles = ['length and angle']\n        break\n      case 3:\n        typesDeQuestionsDisponibles = ['parallelism', 'length and angle']\n        break\n    }\n    const listeTypeDeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions)\n    let objetsEnonceEtCorr, objetsEnonceOnly, objetsCorrectionOnly, paramsEnonce\n    for (let i = 0, texte, texteCorr, figure, transformation, enonceTransformation, d, d1, A, B, C, D, E, imageA, imageB, imageC, figureRetournee, O, poly, imPoly, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n      objetsEnonceOnly = []\n      objetsCorrectionOnly = []\n      objetsEnonceEtCorr = []\n      const lettres = choisitLettresDifferentes(5, 'O')\n      A = point(0, 0, lettres[0], 'below')\n      B = pointAdistance(A, randint(30, 60) / 10, randint(0, 45), lettres[1])\n      C = triangle2points2longueurs(A, B, randint(40, 60) / 10, randint(30, 50) / 10).listePoints[2]\n      C.nom = lettres[2]\n      D = point(0, 0)\n      E = point(0, 0)\n      d1 = droiteParPointEtParallele(C, droite(A, B))\n      poly = polygoneAvecNom(A, B, C) // pour bien placer les labels\n      objetsEnonceEtCorr.push(segment(A, B), afficheLongueurSegment(B, A), poly[1])\n      // We prepare the transformation\n      switch (listeTypeDeTransformations[i]) {\n        case 'symmetryAxial':\n          transformation = 'axial symmetry'\n          enonceTransformation = 'by the axis symmetry $(d)$'\n          d = droite(translation(A, vecteur(-randint(30, 40) / 10, 0)), translation(C, vecteur(-randint(30, 40) / 10, 0)))\n          d.angleAvecHorizontale = d.angleAvecHorizontale + randint(-10, 10)\n          objetsEnonceEtCorr.push(d)\n          imageA = symetrieAxiale(A, d, `${A.nom}'`)\n          imageB = symetrieAxiale(B, d, `${B.nom}'`)\n          imageC = symetrieAxiale(C, d, `${C.nom}'`)\n          if (listeTypeDeQuestions[i] === 'parallelism') {\n            objetsCorrectionOnly.push(...droiteAvecNomLatex(droite(symetrieAxiale(point(d1.x1, d1.y1), d), symetrieAxiale(point(d1.x2, d1.y2), d), '', '#f15929'), '$(d_1\\')$'))\n          }\n          figureRetournee = false\n          break\n        case 'symmetryCentral':\n          transformation = 'central symmetry'\n          enonceTransformation = 'by the symmetry of center $O$'\n          do {\n            O = point(randint(25, 45) / 10, randint(35, 65) / 10, 'O')\n            imageA = rotation(A, O, 180, `${A.nom}'`)\n            imageB = rotation(B, O, 180, `${B.nom}'`)\n            imageC = rotation(C, O, 180, `${C.nom}'`)\n          } while (distancePointDroite(O, d1) < 1 || longueur(O, B) < 1 || Math.abs(Math.round(angle(B, A, imageC)) - 90) > 85)\n          objetsEnonceEtCorr.push(tracePoint(O), labelPoint(O))\n          if (listeTypeDeQuestions[i] === 'parallelism') {\n            objetsCorrectionOnly.push(droite(rotation(point(d1.x1, d1.y1), O, 180), rotation(point(d1.x2, d1.y2), O, 180), '#f15929'))\n          }\n          figureRetournee = true\n          break\n        case 'translation':\n          transformation = 'translation'\n          D = point(B.x + 1, B.y + 8 + randint(-10, 10) / 10, lettres[3])\n          E = point(B.x + 8, B.y + 8 + randint(-20, 20) / 10, lettres[4])\n          enonceTransformation = `by the translation which transforms $${D.nom}$ into $${E.nom}$`\n          imageA = translation2Points(A, D, E, `${A.nom}'`)\n          imageB = translation2Points(B, D, E, `${B.nom}'`)\n          imageC = translation2Points(C, D, E, `${C.nom}'`)\n          objetsEnonceEtCorr.push(vecteur(D, E).representant(D), tracePoint(D, E), labelPoint(D, E))\n          if (listeTypeDeQuestions[i] === 'parallelism') {\n            objetsCorrectionOnly.push(droite(translation2Points(point(d1.x1, d1.y1), D, E), translation2Points(point(d1.x2, d1.y2), D, E), '#f15929'))\n          }\n          break\n      }\n      switch (listeTypeDeQuestions[i]) {\n        case 'parallelism':\n          objetsEnonceEtCorr.push(tracePoint(A, B, C))\n          objetsEnonceEtCorr.push(d1)\n          texte = `The points $${A.nom}'$, $${B.nom}'$ and $${C.nom}'$ are the respective images of $${A.nom}$, $${B.nom}$ and $${C.nom}$ ${enonceTransformation}.<br>`\n          texte += `The line $(d_1)$ is parallel to the segment [$${A.nom + B.nom}$] and passes through the point $${C.nom}$.<br>`\n          figure = 'from the right $(d_1)$'\n          texteCorr = texte\n          texteCorr += `However, the ${transformation} preserves parallelism.<br>`\n          texteCorr += `So the line $(d_1')$ is parallel to the segment [$${A.nom}'${B.nom}'$] and passes through the point $${C.nom}'$.<br>`\n          break\n        case 'length and angle':\n          objetsEnonceEtCorr.push(segment(A, C), segment(B, C))\n          objetsEnonceEtCorr.push(afficheLongueurSegment(C, B))\n          objetsEnonceEtCorr.push(afficheMesureAngle(A, B, C, 'black', 1, Math.round(angle(A, B, C)) + '°'))\n          texte = `The points $${A.nom}'$ and $${B.nom}'$ are the respective images of $${A.nom}$ and $${B.nom}$ ${enonceTransformation}.<br>`\n          texte += `The angle $\\\\widehat{${A.nom + B.nom + C.nom}}$ measures $${texNombre(Math.round(angle(A, B, C)))}$ °.<br>`\n          figure = `of the triangle $${A.nom + B.nom + C.nom}$`\n          texteCorr = texte\n          texteCorr += `However, ${transformation} preserves the angles.<br>`\n          texteCorr += `So the angle $\\\\widehat{${A.nom}'${B.nom}'${C.nom}'}$ also measures $${texNombre(Math.round(angle(A, B, C)))}$ °.<br><br>`\n          texteCorr += `The [$${B.nom + C.nom}$] segment measures $${texNombre(longueur(B, C, 1))}$ cm.<br>`\n          texteCorr += `However, the ${transformation} preserves the lengths.<br>`\n          texteCorr += `So the segment [$${B.nom}'${C.nom}'$] also measures $${texNombre(longueur(B, C, 1))}$ cm.<br>`\n          break\n      }\n      texte += `Complete the ${figure} ${enonceTransformation} image using the conservation properties of the ${transformation} and justifying your actions.<br>`\n      // We apply the transformation\n      imPoly = polygoneAvecNom(imageA, imageB, imageC)\n      const imPolyEnonce = polygoneAvecNom(imageA, imageB)\n      objetsCorrectionOnly.push(imPoly[1])\n      objetsEnonceEtCorr.push(segment(imageA, imageB))\n      objetsEnonceOnly.push(tracePoint(imageA, imageB), imPolyEnonce[1])\n      if (figureRetournee) {\n        objetsEnonceOnly.push(afficheLongueurSegment(imageA, imageB))\n        objetsCorrectionOnly.push(afficheLongueurSegment(imageB, imageA))\n      } else {\n        objetsEnonceOnly.push(afficheLongueurSegment(imageB, imageA))\n        objetsCorrectionOnly.push(afficheLongueurSegment(imageA, imageB))\n      }\n      if (listeTypeDeQuestions[i] === 'length and angle') {\n        objetsCorrectionOnly.push(segment(imageA, imageC, '#f15929'), segment(imageB, imageC, '#f15929'))\n        objetsCorrectionOnly.push(afficheMesureAngle(imageA, imageB, imageC, '#f15929', 1, Math.round(angle(A, B, C)) + '°', { colorArc: '#f15929' }))\n        if (figureRetournee) {\n          objetsCorrectionOnly.push(afficheLongueurSegment(imageC, imageB, '#f15929'))\n        } else {\n          objetsCorrectionOnly.push(afficheLongueurSegment(imageB, imageC, '#f15929'))\n        }\n      } else if (listeTypeDeQuestions[i] === 'parallelism') {\n        objetsEnonceEtCorr.push(tracePoint(imageC))\n        objetsEnonceOnly.push(labelPoint(imageC))\n        // objectsCorrectionOnly.push(tracePoint(imageA, imageB))\n      }\n      const xmin = Math.min(A.x, B.x, C.x, D.x, E.x, imageA.x, imageB.x, imageC.x) - 2\n      const xmax = Math.max(A.x, B.x, C.x, D.x, E.x, imageA.x, imageB.x, imageC.x) + 2\n      const ymin = Math.min(A.y, B.y, C.y, D.x, E.x, imageA.y, imageB.y, imageC.y) - 2\n      const ymax = Math.max(A.y, B.y, C.y, D.x, E.x, imageA.y, imageB.y, imageC.y) + 2\n      // Mathalea2d window parameters for normal statement\n      paramsEnonce = { xmin, ymin, xmax, ymax, pixelsParCm: 20, scale: 1 }\n      // We add the names of the lines if necessary\n      if (listeTypeDeTransformations[i] === 'symmetryAxial') objetsEnonceEtCorr.push(texteParPoint('$(d)$', positionLabelDroite(d, paramsEnonce), 'medium', 'black', 1, 'middle', true))\n      if (listeTypeDeQuestions[i] === 'parallelism') objetsEnonceEtCorr.push(texteParPoint('$(d_1)$', positionLabelDroite(d1, paramsEnonce), 'medium', 'black', 1, 'middle', true))\n      // We add to the text of the statement, the freehand figure and the figure of the statement.\n      texte += mathalea2d(Object.assign({}, fixeBordures([objetsEnonceOnly, objetsEnonceEtCorr])), objetsEnonceOnly, objetsEnonceEtCorr)\n\n      // We add to the text of the correction, the figure of the correction\n      texteCorr += mathalea2d(Object.assign({}, fixeBordures([objetsCorrectionOnly, objetsEnonceEtCorr])), objetsCorrectionOnly, objetsEnonceEtCorr)\n      if (this.questionJamaisPosee(i, texte)) { // <- laisser le i et ajouter toutes les variables qui rendent les exercices différents (par exemple a, b, c et d)\n        this.listeQuestions.push(texte)\n        this.listeCorrections.push(texteCorr)\n        i++\n      }\n      cpt++\n    }\n    listeQuestionsToContenu(this)\n  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