{"version":3,"file":"3G13-Wrdt2MTo.js","sources":["../../src/exercices/3e/3G13.js"],"sourcesContent":["import Algebrite from 'algebrite'\nimport { abs, divide, evaluate, format, fraction, isInteger, max, multiply, pow, round, subtract } from 'mathjs'\nimport { arcPointPointAngle } from '../../lib/2d/cercle.js'\nimport { texteSurArc, texteSurSegment } from '../../lib/2d/codages.js'\nimport { point } from '../../lib/2d/points.js'\nimport { segmentAvecExtremites } from '../../lib/2d/segmentsVecteurs.js'\nimport { labelPoint } from '../../lib/2d/textes.js'\nimport { homothetie, rotation } from '../../lib/2d/transformations.js'\nimport { choice, combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { choisitLettresDifferentes } from '../../lib/outils/aleatoires'\nimport { deprecatedTexFraction } from '../../lib/outils/deprecatedFractions.js'\nimport { texNombre } from '../../lib/outils/texNombre.js'\nimport { fixeBordures, mathalea2d } from '../../modules/2dGeneralites.js'\nimport { context } from '../../modules/context.js'\nimport {\n  gestionnaireFormulaireTexte,\n  listeQuestionsToContenu,\n  randint\n} from '../../modules/outils.js'\nimport Exercice from '../Exercice.js'\n\nexport const titre = 'Homothety (calculations)'\n// eslint-disable-next-line no-debugger\n// debugger\n// Les exports suivants sont optionnels mais au moins la date de publication semble essentielle\nexport const dateDePublication = '28/11/2021' // La date de publication initiale au format 'jj/mm/aaaa' pour affichage temporaire d'un tag\nexport const dateDeModifImportante = '29/01/2023' //  Par EE\n\n/**\n * Calculs dans une homothétie : longueurs, aires.\n * @author Frédéric PIOU\n*/\nexport const uuid = '6f383'\nexport const ref = '3G13'\n\n/**\n * Formattage pour une sortie LaTeX entre $$\n * formatFraction = false : si l'expression est un objet fraction du module mathjs alors elle peut donner l'écriture fractionnaire\n * Pour une fraction négative la sortie est -\\dfrac{6}{7} au lieu de \\dfrac{-6}{7}\n * @author Frédéric PIOU\n */\n\nexport function texNum (expression, formatFraction = false) {\n  if (typeof expression === 'object') {\n    const signe = expression.s === 1 ? '' : '-'\n    if (formatFraction) {\n      expression = expression.d !== 1 ? signe + deprecatedTexFraction(expression.n, expression.d) : signe + expression.n\n      expression = expression.replace(',', '{,}').replace('{{,}}', '{,}')\n    } else {\n      expression = texNombre(evaluate(format(expression)))\n    }\n    // expression = expression.replace(',', '{,}').replace('{{,}}', '{,}') // Deleted by EE because it is not functional in the preceding else.\n  } else {\n    expression = texNombre(parseFloat(Algebrite.eval(expression)))\n  }\n  return expression\n}\n\nexport default function CalculsHomothetie () {\n  Exercice.call(this) // Héritage de la classe Exercice()\n  this.consigne = ''\n  this.nbQuestions = 4 // Nombre de questions par défaut\n  this.nbCols = 0 // Uniquement pour la sortie LaTeX\n  this.nbColsCorr = 0 // Uniquement pour la sortie LaTeX\n  this.tailleDiaporama = 1 // Pour les exercices chronométrés. 50 par défaut pour les exercices avec du texte\n  this.video = '' // Id YouTube ou url\n  this.correctionDetailleeDisponible = true\n  this.correctionDetaillee = true\n  context.isHtml ? (this.spacing = 1.5) : (this.spacing = 0)\n  context.isHtml ? (this.spacingCorr = 1.5) : (this.spacingCorr = 0)\n  this.sup = 12 // Type d'exercice\n  this.sup2 = 3 // 1 : Homothéties de rapport positif, 2: de rapport négatif 3 : mélange\n  this.sup3 = 1 // Choix des valeurs\n  this.sup4 = true // Affichage des figures facultatives dans l'énoncé (en projet)\n\n  this.besoinFormulaireTexte = [\n    'Type of questions', [\n      'Numbers separated by hyphens',\n      '1: Calculate the ratio',\n      '2: Calculate an image length',\n      '3: Calculate an antecedent length',\n      '4: Calculate an image length (two steps)',\n      '5: Calculate an antecedent length (two steps)',\n      '6: Calculate an image area',\n      '7: Calculate an antecedent area',\n      '8: Calculate the ratio from the areas',\n      '9: Calculate the ratio knowing OA and AA\\'',\n      '10: Framing the report k',\n      '11: Frame the report k knowing OA and AA\\'',\n      '12: Mixture'\n    ].join('\\not')\n  ]\n  this.besoinFormulaire2Numerique = [\n    'Report sign',\n    3,\n    '1: positive\\n2: negative\\n3: mixture'\n  ]\n  this.besoinFormulaire3Numerique = [\n    'Choice of values',\n    3,\n    '1: k is decimal (0.1 < k < 4) \\n2: k is a fraction k = a/b with (a,b) in [1;9]\\n3: k is a fraction and the measurements are integers'\n  ]\n  this.besoinFormulaire4CaseACocher = ['Figure in statement (1-5,9-11)', false]\n  this.nouvelleVersion = function () {\n    this.listeQuestions = [] // Liste de questions\n    this.listeCorrections = [] // Liste de questions corrigées\n\n    const typeQuestionsDisponibles = ['report', 'picture', 'antecedent', 'image2steps', 'background2steps', 'areaImage', 'areaAntecedent', 'areaReport', 'report2', 'frame', 'framerk2']\n    const listeTypeQuestions = gestionnaireFormulaireTexte({ saisie: this.sup, min: 1, max: 11, melange: 12, defaut: 12, nbQuestions: this.nbQuestions, listeOfCase: typeQuestionsDisponibles })\n    const kEstEntier = this.sup3 > 1\n    const valeursSimples = this.sup3 === 3\n    for (let i = 0, approx, environ, melange, donnee1, donnee2, donnee3, donnees, texte, texteCorr, cpt = 0; i < this.nbQuestions && cpt < 50;) { // Boucle principale où i+1 correspond au numéro de la question\n      const lettres = choisitLettresDifferentes(5, ['P', 'Q', 'U', 'V', 'W', 'X', 'Y', 'Z'])\n      const A = lettres[0]; const hA = lettres[1]; const O = lettres[2]; const B = lettres[3]; const hB = lettres[4]\n      const ks = fraction(choice([[1], [-1], [-1, 1]][this.sup2 - 1]))\n      let k = fraction(1, 1)\n      while (abs(k).toString() === '1') {\n        k = kEstEntier ? multiply(fraction(randint(1, 9), randint(1, 9)), ks) : multiply(fraction(choice([randint(15, 40) / 10, randint(1, 9) / 10])), ks)\n      }\n      let absk = abs(k)\n      const agrandissement = evaluate(absk > 1)\n      const kpositif = evaluate(k > 0)\n      const longueurEntiere = valeursSimples ? fraction(randint(1, 19)) : fraction(randint(11, 99))\n      let OA = multiply(agrandissement ? divide(longueurEntiere, 10) : longueurEntiere, 10 ** (valeursSimples) * absk.d ** (kEstEntier))\n      let OhA = multiply(k, OA)\n      let OB = multiply(divide(randint(10, 99, [parseInt(longueurEntiere.toString())]), fraction(10)), 10 ** (valeursSimples) * absk.d ** (kEstEntier))\n      let OhB = multiply(k, OB)\n      let AhA = subtract(OhA, OA)\n      let kAire = fraction(choice([randint(1, 4) + 0.5 + choice([0, 0.5]), randint(1, 9) / 10]))\n      let Aire = valeursSimples ? fraction(randint(10, 99)) : fraction(randint(100, 999) / 10)\n      let hAire = multiply(pow(kAire, 2), Aire)\n      let hAireArrondie = round(hAire, 2)\n      const plusgrandque = agrandissement ? '>' : '<'\n      const unAgrandissement = agrandissement ? 'an agrandissement' : 'a discount'\n      const intervallek = agrandissement ? (kpositif ? '$k > 1$' : '$k < -1$') : (kpositif ? '$0 < k < 1$' : '$-1 < k < 0$')\n      const positif = kpositif ? 'positive' : 'negative'\n      const signek = kpositif ? '' : '-'\n      const lopposede = kpositif ? '' : 'opposite of'\n      const lopposedu = kpositif ? 'THE' : 'the opposite of'\n      const derapportpositifet = this.sup4 ? '' : `${positif} report and`\n      const inNotin = kpositif ? '\\\\in' : '\\\\notin'\n      const illustrerParUneFigureAMainLevee = this.sup4 ? '' : 'Illustrate the situation with a freehand figure.<br>'\n      let kinverse = abs(divide(1, k))\n      const OhAdivkInversed = texNum(abs(divide(OhA, kinverse.d)))\n      const OhBdivkInversed = texNum(abs(divide(OhB, kinverse.d)))\n      const largeurFigure = divide(10, max(abs(OA), abs(OhA), abs(AhA)))\n      let testFigureCorrigee = true\n      let correctionOhA = OhA\n      let correctionOA = OA\n      if (evaluate(abs(k) < 0.3)) {\n        correctionOhA = multiply(multiply(fraction(3, 10), OA), (-1) ** evaluate(k < 0))\n      } else if (evaluate(abs(k) < 1 && abs(k) > 0.7)) {\n        correctionOhA = multiply(multiply(fraction(7, 10), OA), (-1) ** evaluate(k < 0))\n      } else if (evaluate(abs(k) > 1 && abs(k) < 1.3)) {\n        correctionOhA = multiply(multiply(fraction(13, 10), OA), (-1) ** evaluate(k < 0))\n      } else if (evaluate(abs(k) > 4)) {\n        correctionOA = multiply(fraction(2, 1), OA)\n      } else {\n        testFigureCorrigee = false\n      }\n      const figurealechelle = !(testFigureCorrigee && this.sup4) || [4, 5, 6, 7, 8].includes(listeTypeQuestions[i]) ? '' : '(Figure is not to scale.)'\n      const figurealechelle2 = !(this.sup4) ? '' : '(Figure is not to scale.)'\n      let figure = {\n        O: point(0, 0, `${O}`),\n        A: point(multiply(correctionOA, largeurFigure).valueOf(), 0, `${A}`, 'below'),\n        hA: point(multiply(correctionOhA, largeurFigure).valueOf(), 0, `${hA}`, kpositif ? 'below' : 'above')\n      }\n      figure = Object.assign({}, figure, {\n        B: homothetie(rotation(figure.A, figure.O, 40), figure.O, 1.2, `${B}`),\n        hB: homothetie(rotation(figure.hA, figure.O, 40), figure.O, 1.2, `${hB}`, kpositif ? 'above' : 'below')\n      })\n      kinverse = { tex: texNum(kinverse, kEstEntier), n: kinverse.n, d: kinverse.d }\n      OhA = texNum(abs(OhA))\n      const OhAtimeskinverse = (valeursSimples && !isInteger(absk)) ? `=${OhA}\\\\times ${kinverse.tex}` + (kinverse.d !== 1 ? `=\\\\dfrac{${OhA}}{${kinverse.d}}\\\\times ${kinverse.n} = ${OhAdivkInversed}\\\\times ${kinverse.n}` : '') : ''\n      OhB = texNum(abs(OhB))\n      const OhBtimeskinverse = (valeursSimples && !isInteger(absk)) ? `=${OhB}\\\\times ${kinverse.tex}` + (kinverse.d !== 1 ? `=\\\\dfrac{${OhB}}{${kinverse.d}}\\\\times ${kinverse.n} = ${OhBdivkInversed}\\\\times ${kinverse.n}` : '') : ''\n      hAire = texNum(hAire)\n      hAireArrondie = texNum(hAireArrondie)\n      k = texNum(k, kEstEntier)\n      kAire = texNum(kAire, kEstEntier)\n      const parentheseskAire = (absk.d === 1 || this.sup3 === 1) && kpositif ? signek + kAire : String.raw`\\left(${signek}${kAire}\\right)`\n      absk = texNum(absk, kEstEntier)\n      OA = texNum(OA)\n      AhA = texNum(abs(AhA))\n      OB = texNum(OB)\n      Aire = texNum(Aire)\n      const calculsOhA = !kpositif ? `${hA}${A} - ${O}${A} = ${AhA} - ${OA}` : agrandissement ? `${O}${A} + ${A}${hA} = ${OA} + ${AhA} ` : `${O}${A} - ${A}${hA} = ${OA} - ${AhA}`\n      figure = Object.assign({}, figure, {\n        segmentOA: segmentAvecExtremites(figure.O, figure.A),\n        segmentOhA: segmentAvecExtremites(figure.O, figure.hA),\n        segmentOB: segmentAvecExtremites(figure.O, figure.B),\n        segmentOhB: segmentAvecExtremites(figure.O, figure.hB)\n      })\n      figure = Object.assign({}, figure, {\n        arcOA: agrandissement || !kpositif ? figure.A : arcPointPointAngle(figure.O, figure.A, 60, false),\n        arcOhA: !agrandissement || !kpositif ? figure.hA : arcPointPointAngle(figure.O, figure.hA, 60, false),\n        arcOB: agrandissement || !kpositif ? figure.B : arcPointPointAngle(figure.B, figure.O, 60, false),\n        arcOhB: !agrandissement || !kpositif ? figure.hB : arcPointPointAngle(figure.hB, figure.O, 60, false),\n        arcAhA: kpositif ? figure.A : arcPointPointAngle(figure.hA, figure.A, 60, false),\n        legendeOA: agrandissement || !kpositif ? texteSurSegment(`${OA.replace('{,}', ',')} cm`, figure.A, figure.O, 'black', 0.30) : texteSurArc(`${OA.replace('{,}', ',')} cm`, figure.O, figure.A, 60, 'black', 0.30),\n        legendeOhA: !agrandissement || !kpositif ? texteSurSegment(`${OhA.replace('{,}', ',')} cm`, figure.hA, figure.O, 'black', 0.30) : texteSurArc(`${OhA.replace('{,}', ',')} cm`, figure.O, figure.hA, 60, 'black', 0.30),\n        legendeOB: agrandissement || !kpositif ? texteSurSegment(`${OB.replace('{,}', ',')} cm`, figure.O, figure.B, 'black', 0.30) : texteSurArc(`${OB.replace('{,}', ',')} cm`, figure.B, figure.O, 60, 'black', 0.30),\n        legendeOhB: !agrandissement || !kpositif ? texteSurSegment(`${OhB.replace('{,}', ',')} cm`, figure.O, figure.hB, 'black', 0.30) : texteSurArc(`${OhB.replace('{,}', ',')} cm`, figure.hB, figure.O, 60, 'black', 0.30),\n        legendeAhA: kpositif ? texteSurSegment(`${AhA.replace('{,}', ',')} cm`, figure.hA, figure.A, 'black', 0.30) : texteSurArc(`${AhA.replace('{,}', ',')} cm`, figure.hA, figure.A, 60, 'black', 0.30)\n      })\n      figure = Object.assign({}, figure, {\n        legendeOAi: agrandissement || !kpositif ? texteSurSegment('?', figure.O, figure.A, 'black', 0.30) : texteSurArc('?', figure.O, figure.A, 60, 'black', 0.30),\n        legendeOhAi: !agrandissement || !kpositif ? texteSurSegment('?', figure.O, figure.hA, 'black', 0.30) : texteSurArc('?', figure.O, figure.hA, 60, 'black', 0.30),\n        legendeOBi: agrandissement || !kpositif ? texteSurSegment('?', figure.O, figure.B, 'black', 0.30) : texteSurArc('?', figure.B, figure.O, 60, 'black', 0.30),\n        legendeOhBi: !agrandissement || !kpositif ? texteSurSegment('?', figure.O, figure.hB, 'black', 0.30) : texteSurArc('?', figure.hB, figure.O, 60, 'black', 0.30)\n      })\n      figure.arcOA.pointilles = 5\n      figure.arcOhA.pointilles = 5\n      figure.arcOB.pointilles = 5\n      figure.arcOhB.pointilles = 5\n      figure.arcAhA.pointilles = 5\n      // const fscale = context.isHtml ? kpositive? 1: 0.7: kpositive? 0.7:0.5\n      let objetsEnonce = []\n      const fscale = context.isHtml ? 1 : kpositif ? 0.7 : 0.6\n\n      const flabelsRapport = labelPoint(figure.O, figure.A, figure.hA)\n      objetsEnonce = [figure.segmentOA, figure.segmentOhA, figure.legendeOA, figure.legendeOhA]\n      if (figure.arcOA.typeObjet !== 'point') objetsEnonce.push(figure.arcOA)\n      if (figure.arcOhA.typeObjet !== 'point') objetsEnonce.push(figure.arcOhA)\n      let frapport = mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), { style: 'inline', scale: fscale }), objetsEnonce, flabelsRapport)\n      frapport = { enonce: (this.sup4 ? '<br>' + frapport : ''), solution: frapport }\n\n      const flabelsImage = labelPoint(figure.O, figure.A, figure.hA)\n      objetsEnonce = [figure.segmentOA, figure.segmentOhA, figure.legendeOA, figure.legendeOhAi]\n      if (figure.arcOA.typeObjet !== 'point') objetsEnonce.push(figure.arcOA)\n      if (figure.arcOhA.typeObjet !== 'point') objetsEnonce.push(figure.arcOhA)\n      let fImage = mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), { style: 'inline', scale: fscale }), objetsEnonce, flabelsImage)\n      fImage = { enonce: (this.sup4 ? fImage : ''), solution: fImage }\n\n      const flabelsAntecedent = labelPoint(figure.O, figure.A, figure.hA)\n      objetsEnonce = [figure.segmentOA, figure.segmentOhA, figure.legendeOhA]\n      if (figure.A.typeObjet !== 'point') objetsEnonce.push(figure.A)\n      if (figure.O.typeObjet !== 'point') objetsEnonce.push(figure.O)\n      if (figure.hA.typeObjet !== 'point') objetsEnonce.push(figure.hA)\n      if (figure.arcOhA.typeObjet !== 'point') objetsEnonce.push(figure.arcOhA)\n      let fAntecedent = mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), { style: 'inline', scale: fscale }), objetsEnonce, flabelsAntecedent)\n      fAntecedent = { enonce: (this.sup4 ? fAntecedent : ''), solution: fAntecedent }\n\n      const flabelsImage2etapes = labelPoint(figure.O, figure.A, figure.hA, figure.B, figure.hB)\n      objetsEnonce = [figure.segmentOA, figure.segmentOhA, figure.segmentOB, figure.segmentOhB, figure.legendeOA, figure.legendeOhA, figure.legendeOB]\n      if (figure.A.typeObjet !== 'point') objetsEnonce.push(figure.A)\n      if (figure.O.typeObjet !== 'point') objetsEnonce.push(figure.O)\n      if (figure.hA.typeObjet !== 'point') objetsEnonce.push(figure.hA)\n      if (figure.B.typeObjet !== 'point') objetsEnonce.push(figure.B)\n      if (figure.hB.typeObjet !== 'point') objetsEnonce.push(figure.hB)\n      if (figure.arcOA.typeObjet !== 'point') objetsEnonce.push(figure.arcOA)\n      if (figure.arcOB.typeObjet !== 'point') objetsEnonce.push(figure.arcOB)\n      if (figure.arcOhA.typeObjet !== 'point') objetsEnonce.push(figure.arcOhA)\n      if (figure.arcOhB.typeObjet !== 'point') objetsEnonce.push(figure.arcOhB)\n      let fImage2etapes = mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), { style: 'inline', scale: fscale }), objetsEnonce, flabelsImage2etapes)\n      fImage2etapes = { enonce: (this.sup4 ? fImage2etapes : ''), solution: fImage2etapes }\n\n      const flabelsAntecedent2etapes = labelPoint(figure.O, figure.A, figure.hA, figure.B, figure.hB)\n      objetsEnonce = [figure.segmentOA, figure.segmentOhA, figure.segmentOB, figure.segmentOhB, figure.legendeOBi, figure.legendeOhB, figure.legendeOA, figure.legendeOhA]\n      if (figure.arcOA.typeObjet !== 'point') objetsEnonce.push(figure.arcOA)\n      if (figure.arcOhA.typeObjet !== 'point') objetsEnonce.push(figure.arcOhA)\n      if (figure.arcOB.typeObjet !== 'point') objetsEnonce.push(figure.arcOB)\n      if (figure.arcOhB.typeObjet !== 'point') objetsEnonce.push(figure.arcOhB)\n      let fAntecedent2etapes = mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), { style: 'inline', scale: fscale }), objetsEnonce, flabelsAntecedent2etapes)\n      fAntecedent2etapes = { enonce: (this.sup4 ? fAntecedent2etapes : ''), solution: fAntecedent2etapes }\n\n      objetsEnonce = [figure.segmentOA, figure.segmentOhA, figure.legendeOA, figure.legendeOhA, figure.legendeAhA]\n      if (figure.arcOA.typeObjet !== 'point') objetsEnonce.push(figure.arcOA)\n      if (figure.arcOhA.typeObjet !== 'point') objetsEnonce.push(figure.arcOhA)\n      if (figure.arcAhA.typeObjet !== 'point') objetsEnonce.push(figure.arcAhA)\n      let frapport2 = mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), { style: 'inline', scale: fscale }), objetsEnonce, flabelsRapport)\n      frapport2 = { enonce: (this.sup4 ? '<br>' + frapport2 : ''), solution: frapport2 }\n      switch (listeTypeQuestions[i]) {\n        case 'report': // cas 1\n          donnees = [String.raw`${O}${hA} = ${OhA}\\text{ cm}`, String.raw`${O}${A} = ${OA}\\text{ cm}`]\n          melange = combinaisonListes([0, 1])\n          donnee1 = donnees[melange[0]]\n          donnee2 = donnees[melange[1]]\n          texte = String.raw`$${hA}$ is the image of $${A}$ by a scaling ${derapportpositifet} with center $${O}$ such that $ {${donnee1}}$ and $ {${donnee2}}$.<br>${illustrerParUneFigureAMainLevee} Calculate the ratio $k$ of this scaling ${figurealechelle}.${frapport.enonce}`\n          texteCorr = String.raw`\n                $k=${signek}\\dfrac{${O}${hA}}{${O}${A}} = ${signek}\\dfrac{${OhA}}{${OA}} = ${k}$.\n                `\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`$[${O}${hA}]$ is the image of $[${O}${A}]$ and $${O} ${hA} ${plusgrandque} ${O} ${A}$ so it is ${unAgrandissement} and we have ${intervallek}.<br> ${frapport.solution}`\n            texteCorr += String.raw`<br>The ratio of this homothety is ${lopposedu} quotient of the length of a segment \"at arrival\" by its length \"at departure\".<br>Let $k=${signek}\\dfrac{${O}${hA}}{${O}${A}} = ${signek}\\ dfrac{${OhA}}{${OA}} = ${k}$.`\n          }\n          break\n        case 'picture': // cas 2\n          texte = String.raw`$${hA}$ is the image of $${A}$ by a homothety of center $${O}$ and ratio $k=${k}$such that $ {${O}${A} = ${OA}\\text{ cm}}$.<br>${illustrerParUneFigureAMainLevee}Calculate $${O}${hA}$ ${figurealechelle}. <br>${fImage.enonce}`\n          texteCorr = String.raw`\n                $${O}${hA}= ${absk} \\times ${OA} =  ${OhA}~\\text{cm}$.\n                `\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`\n                ${intervallek} donc $[${O}${hA}]$ est ${unAgrandissement} de $[${O}${A}]$.\n                <br>${fImage.solution}\n                `\n            texteCorr += String.raw`<br>A ${positif} ratio scaling is a transformation which multiplies all the lengths by ${lopposede} its ratio.<br>Let $${O}${hA} = ${signek}k \\times ${O}${A}$.<br>So $${O}${hA}= ${absk} \\times ${OA} = ${OhA}~\\text{cm }$.`\n          }\n          break\n        case 'antecedent': // cas 3\n          texte = String.raw`$${hA}$ is the image of $${A}$ by a homothety of center $${O}$ and ratio $k=${k}$ such that $ {${O}${hA} = ${OhA}\\text{ cm}}$.<br>${illustrerParUneFigureAMainLevee}Calculate $${O}${A}$ ${figurealechelle}. <br>${fAntecedent.enonce}`\n          texteCorr = String.raw`$${O}${A}=\\dfrac{${O}${hA}}{${absk}}=\\dfrac{${OhA}}{${absk}} = ${OA}~\\text{cm}$.`\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`\n                ${intervallek} donc $[${O}${hA}]$ est ${unAgrandissement} de $[${O}${A}]$.\n                <br>${fAntecedent.solution}\n                `\n            texteCorr += String.raw`<br>A ${positif} ratio scaling is a transformation which multiplies all the lengths by ${lopposede} its ratio.<br>Let $${O}${hA} = ${signek}k \\times ${O}${A}$.<br>So $${O}${A}=\\dfrac{${O}${hA}}{${signek}k}=\\dfrac {${OhA}}{${absk}} ${OhAtimeskinverse} = ${OA}~\\text{cm}$.`\n          }\n          break\n        case 'image2steps': // cas 4\n          donnees = [String.raw`${O}${B} = ${OB}\\text{ cm}`, String.raw`${O}${hA} = ${OhA}\\text{ cm}`, String.raw`${O}${A} = ${OA}\\text{ cm}`]\n          melange = combinaisonListes([0, 1, 2])\n          donnee1 = donnees[melange[0]]\n          donnee2 = donnees[melange[1]]\n          donnee3 = donnees[melange[2]]\n          texte = String.raw`$${hA}$ and $${hB}$ are the respective images of $${A}$ and $${B}$ by a homothety${derapportpositifet} with center $${O}$ such that $ {${donnee1}}$, $ {${donnee2}}$ and $ {${donnee3}}$.<br>${illustrerParUneFigureAMainLevee}Calculate $${O}${hB}$ ${figurealechelle2}.<br>${fImage2etapes.enonce}`\n          texteCorr = String.raw`\n                    $k=${signek}\\dfrac{${O}${hA}}{${O}${A}} = ${signek}\\dfrac{${OhA}}{${OA}} = ${k}$ et $${O}${hB}= ${absk} \\times ${OB} = ${OhB}~\\text{cm}$.\n                    `\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`$[${O}${hA}]$ is the image of $[${O}${A}]$ and $${O} ${hA} ${plusgrandque} ${O} ${A}$ so it is ${unAgrandissement} and we have ${intervallek}.<br>${fImage2etapes.solution}`\n            texteCorr += String.raw`<br>The ratio of this homothety is${lopposedu} quotient of the length of a segment \"at arrival\" by its length \"at departure\".<br>Let $k=${signek}\\dfrac{${O}${hA}}{${O}${A}} = ${signek}\\ dfrac{${OhA}}{${OA}} = ${k}$.<br>$[${O}${hB}]$ is the image of $[${O}${B}]$.<br>But a scaling of ratio ${positif} is a transformation which multiplies all the lengths by ${lopposede} its ratio. <br>Let $${O}${hB}= ${signek}k \\times ${O}${B}$.<br>So $${O}${hB}= ${absk} \\times ${OB} = ${OhB}~\\text{cm}$.`\n          }\n          break\n        case 'background2steps': // cas 5\n          donnees = [String.raw`${O}${hB} = ${OhB}\\text{ cm}`, String.raw`${O}${hA} = ${OhA}\\text{ cm}`, String.raw`${O}${A} = ${OA}\\text{ cm}`]\n          melange = combinaisonListes([0, 1, 2])\n          donnee1 = donnees[melange[0]]\n          donnee2 = donnees[melange[1]]\n          donnee3 = donnees[melange[2]]\n          texte = String.raw`$${hA}$ and $${hB}$ are the respective images of $${A}$ and $${B}$ by a ${derapportpositifet} scale with center $${O}$ such that $ {${donnee1}}$, $ {${donnee2}}$ and $ {${donnee3}}$.<br>${illustrerParUneFigureAMainLevee}Calculate $${O}${B}$ ${figurealechelle2}.<br>${fAntecedent2etapes.enonce}`\n          texteCorr = String.raw`$k=${signek}\\dfrac{${O}${hA}}{${O}${A}} = ${signek}\\dfrac{${OhA}}{${OA}} = ${k}$and $${O}${B}=\\dfrac{${O}${hB}}{${absk}}=\\dfrac{${OhB}}{${absk}} = ${OB}~\\ text{cm}$.`\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`$[${O}${hA}]$ is the image of $[${O}${A}]$ and $${O} ${hA} ${plusgrandque} ${O} ${A}$ so it is ${unAgrandissement} and we have ${intervallek}.<br>${fAntecedent2etapes.solution}`\n            texteCorr += String.raw`<br>The ratio of this homothety is ${lopposedu} quotient of the length of a segment \"at arrival\" by its length \"at departure\".<br>Let $k=${signek}\\dfrac{${O}${hA}}{${O}${A}} = ${signek}\\ dfrac{${OhA}}{${OA}} = ${k}$.<br>$[${O}${hB}]$ is the image of $[${O}${B}]$.<br>But a scaling of ratio ${positif} is a transformation which multiplies all the lengths by ${lopposede} its ratio. <br>Let $${O}${hB} = ${signek}k \\times ${O}${B}$.<br>So $${O}${B}=\\dfrac{${O}${hB}}{${signek}k}=\\dfrac{${OhB}}{${absk}} ${OhBtimeskinverse} = ${OB}~\\text{cm}$.`\n          }\n          break\n        case 'areaImage': // cas 6\n          environ = (hAire === hAireArrondie) ? '' : 'approximately'\n          approx = (environ === 'approximately') ? '\\\\approx' : '='\n          texte = String.raw`A figure has the area $ {${Aire}\\text{ cm}^2}$.<br>Calculate the area of its image by a scale of ratio $${signek}${kAire}$ (round to the nearest $ {\\text{mm}^2}$ close if necessary).`\n          texteCorr = String.raw`\n                $ {${parentheseskAire}^2 \\times ${Aire} ${approx} ${hAireArrondie}~\\text{cm}^2}$\n                `\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`A ${positif} ratio scaling is a transformation that multiplies all areas by the square of its ratio.<br>$${parentheseskAire}^2 \\times ${Aire} = ${hAire}$<br>So the area of the image in this figure is ${environ} $ {${hAireArrondie}~\\text{cm}^2}$.`\n          }\n          break\n        case 'areaAntecedent': // cas 7\n          texte = String.raw`The image of a figure by a homothety of ratio $${signek}${kAire}$ has the area $ {${hAire}\\text{ cm}^2}$.<br>Calculate the area of the starting figure.`\n          texteCorr = String.raw`$ {\\dfrac{${hAire}}{${parentheseskAire}^2} = ${Aire}~\\text{cm}^2}$`\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`A ${positif} ratio scaling is a transformation which multiplies all the areas by the square of its ratio.<br>Let $\\mathscr{A}$ denote the area of the starting figure.<br>Hence $${parentheseskAire}^2 \\times \\mathscr{A} = ${hAire}$.<br>Then $\\mathscr{A}=\\dfrac{${hAire}}{${parentheseskAire}^2} = ${Aire}$.<br>So the area of the starting figure is $ {${Aire}~\\text{cm}^2}$.`\n          }\n          break\n        case 'areaReport': // cas 8\n          texte = String.raw`A figure and its image by a ${positif} ratio scale have respectively areas $ {${Aire}\\text{ cm}^2}$ and $ {${hAire}\\text{ cm}^2}$.<br>Calculate the ratio of the homothety.`\n          texteCorr = String.raw`$ {k=${signek}\\sqrt{\\dfrac{${hAire}}{${Aire}}} = ${signek}${kAire}}$`\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`A ${positif} ratio scale is a transformation which multiplies all the areas by the square of its ratio.<br>Let $k$ be the ratio of this scale. We therefore have $k^2 \\times ${Aire} = ${hAire}$, or again $k ^2=\\dfrac{${hAire}}{${Aire}}$.<br>Hence $ {k=${signek}\\sqrt{\\dfrac{${hAire}}{${Aire}}} = ${signek}${kAire}}$.`\n          }\n          break\n        case 'report2': // cas 9\n          donnees = [String.raw`${A}${hA} = ${AhA}\\text{ cm}`, String.raw`${O}${A} = ${OA}\\text{ cm}`]\n          melange = combinaisonListes([0, 1])\n          donnee1 = donnees[melange[0]]\n          donnee2 = donnees[melange[1]]\n          texte = String.raw`$${hA}$ is the image of $${A}$ by a scaling ${derapportpositifet} with center $${O}$ such that $ {${donnee1}}$ and $ {${donnee2}}$.<br>${illustrerParUneFigureAMainLevee} Calculate the ratio $k$ of this scaling ${figurealechelle}.${frapport2.enonce}`\n          texteCorr = String.raw`\n                $k=${signek}\\dfrac{${O}${hA}}{${O}${A}} = ${signek}\\dfrac{${OhA}}{${OA}} = ${k}$.\n                `\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`$${O}${hA} = ${calculsOhA} = ${OhA}\\text{ cm}$<br>$[${O}${hA}]$ is the image of $[${O}${A}]$ and $${O} ${hA} ${plusgrandque} ${O} ${A}$ so it is ${unAgrandissement} and we have ${intervallek}.<br> ${frapport.solution}`\n            texteCorr += String.raw`<br>The ratio of this homothety is ${lopposedu} quotient of the length of a segment \"at arrival\" by its length \"at departure\".<br>Let $k=${signek}\\dfrac{${O}${hA}}{${O}${A}} = ${signek}\\ dfrac{${OhA}}{${OA}} = ${k}$.`\n          }\n          break\n        case 'frame': // cas 10\n          donnees = [String.raw`${O}${hA} = ${OhA}\\text{ cm}`, String.raw`${O}${A} = ${OA}\\text{ cm}`]\n          melange = combinaisonListes([0, 1])\n          donnee1 = donnees[melange[0]]\n          donnee2 = donnees[melange[1]]\n          texte = String.raw`$${hA}$ is the image of $${A}$ by a homothety ${derapportpositifet} with center $${O}$ such that $ {${donnee1}}$ and $ {${donnee2}}$.<br>${illustrerParUneFigureAMainLevee}Without performing calculations, what can we say about the ratio $k $ of this homothety?(choose the correct answer)<br>$\\square\\hphantom{a} k<-1 \\hspace{1cm} \\square\\hphantom{a} -1 < k < 0 \\hspace{1cm} \\ square\\hphantom{a} 0 < k < 1 \\hspace{1cm} \\square\\hphantom{a} k > 1$.<br>${figurealechelle}${frapport.enonce}`\n          texteCorr = String.raw`\n                $${intervallek}$.\n                `\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`$[${O}${hA}]$ is the image of $[${O}${A}]$ and $${O} ${hA} ${plusgrandque} ${O} ${A}$ so it is ${unAgrandissement}.<br>Moreover $${hA}${inNotin}[${O};${A})$ therefore ${intervallek}.<br> ${frapport.solution}`\n          }\n          break\n        case 'framerk2': // cas 11\n          donnees = [String.raw`${A}${hA} = ${AhA}\\text{ cm}`, String.raw`${O}${A} = ${OA}\\text{ cm}`]\n          melange = combinaisonListes([0, 1])\n          donnee1 = donnees[melange[0]]\n          donnee2 = donnees[melange[1]]\n          texte = String.raw`$${hA}$ is the image of $${A}$ by a homothety ${derapportpositifet} with center $${O}$ such that $ {${donnee1}}$ and $ {${donnee2}}$.<br>${illustrerParUneFigureAMainLevee}Without performing calculations, what can we say about the ratio $k $ of this homothety?(choose the correct answer)<br>$\\square\\hphantom{a} k<-1 \\hspace{1cm} \\square\\hphantom{a} -1 < k < 0 \\hspace{1cm} \\ square\\hphantom{a} 0 < k < 1 \\hspace{1cm} \\square\\hphantom{a} k > 1$.<br>${figurealechelle}${frapport2.enonce}`\n          texteCorr = String.raw`$${intervallek}$.`\n          if (this.correctionDetaillee) {\n            texteCorr = String.raw`$${O}${hA} = ${calculsOhA} = ${OhA}\\text{ cm}$<br>$[${O}${hA}]$ is the image of $[${O}${A}]$ and $${O} ${hA} ${plusgrandque} ${O} ${A}$ so it is ${unAgrandissement}.<br>Plus $ ${hA}${inNotin}[${O};${A})$ therefore ${intervallek}.<br> ${frapport.solution}`\n          }\n          break\n      }\n      if (this.questionJamaisPosee(i, k)) {\n    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