File: /home/mmtprep/public_html/mathzen.mmtprep.com/assets/2G30-7-5c9mAaJb.js.map
{"version":3,"file":"2G30-7-5c9mAaJb.js","sources":["../../src/exercices/2e/2G30-7.js"],"sourcesContent":["import { droite } from '../../lib/2d/droites.js'\nimport { point, tracePoint } from '../../lib/2d/points.js'\nimport { repere } from '../../lib/2d/reperes.js'\nimport { segment } from '../../lib/2d/segmentsVecteurs.js'\nimport { labelPoint, texteParPosition } from '../../lib/2d/textes.js'\nimport { texFractionReduite } from '../../lib/outils/deprecatedFractions.js'\nimport { ecritureAlgebrique, reduireAxPlusB } from '../../lib/outils/ecritures'\nimport { abs } from '../../lib/outils/nombres'\nimport { pgcd } from '../../lib/outils/primalite'\nimport Exercice from '../deprecatedExercice.js'\nimport { colorToLatexOrHTML, mathalea2d } from '../../modules/2dGeneralites.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.js'\nimport { context } from '../../modules/context.js'\nimport Decimal from 'decimal.js'\nimport { setReponse } from '../../lib/interactif/gestionInteractif.js'\n\nexport const titre = 'Determine a reduced equation from its graphical representation'\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\nexport const amcReady = true\nexport const amcType = 'AMCHybride'\n/**\n */\nexport const uuid = '41e6f'\nexport const ref = '2G30-7'\nexport default function Lecturegraphiquedeaetb () {\n Exercice.call(this)\n\n this.nbQuestions = 3// On complète le nb de questions\n this.nbCols = 1\n this.nbColsCorr = 1\n this.tailleDiaporama = 3\n this.video = ''\n this.spacing = 1\n this.spacingCorr = 1\n this.spacingCorr = 1\n this.sup = 1\n\n this.nouvelleVersion = function () {\n this.sup = parseInt(this.sup)\n this.listeQuestions = []\n this.listeCorrections = []\n this.autoCorrection = []\n // let AvailableQuestionTypes = []\n // typesOfAvailableQuestions = []// We complete according to the number of cases in the exo (switch)\n\n // const listTypeOfQuestions = combinationLists(availableQuestionTypes, this.nbQuestions)\n\n for (let i = 0, a, b, r, c, d, s1, s2, t, l, o, texte, texteCorr, cpt = 0;\n i < this.nbQuestions && cpt < 50;) { // on rajoute les variables dont on a besoin\n if (this.sup === 1) {\n a = randint(-4, 4) // coefficient directeur\n b = randint(-5, 5) // ordonnée à l'origine\n if (a === 0 && b === 0) {\n a = 1\n }// On évite la situation de double nullité\n r = repere({\n xMin: -8,\n xMax: 8,\n yMin: -8,\n yMax: 8,\n yLabelEcart: 0.8,\n yLabelDistance: 2,\n xLabelDistance: 2,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -8,\n grilleSecondaireYMax: 8,\n grilleSecondaireXMin: -8,\n grilleSecondaireXMax: 8\n })\n c = droite(a, -1, b) // On définit l'objet qui tracera la courbe dans le repère\n c.color = colorToLatexOrHTML('red')\n c.epaisseur = 2\n o = texteParPosition('O', -0.5, -0.5, 'medium', 'black', 1)\n texte = 'From the graphic representation of the line below, give by graphic reading its reduced equation.<br><br>'\n texte += mathalea2d({\n xmin: -8,\n ymin: -8,\n xmax: 8,\n ymax: 8,\n scale: 0.5\n }, r, c, o)// On trace le graphique\n if (a === 0) {\n texteCorr = 'We observe that the line is horizontal.'\n texteCorr += `<br>The line is the set of points having as ordinate: $${b}$`\n texteCorr += `<br>The reduced equation of this line is therefore: $y=${b}$`\n } else {\n texteCorr = 'We know that the reduced equation of a non-vertical line is of the form: $y= ax+b$ with $a$ and $b$ two real numbers not both zero.<br>'\n texteCorr += 'The first coefficient to read graphically is $b$, the intercept of the line.<br>'\n texteCorr += 'It is the ordinate of the point of intersection of the line with the ordinate axis.<br>'\n texteCorr += `We read here that the point $(0,${b}) \\\\in (d)$.<br>`\n texteCorr += `We can then conclude that the intercept is: $b=${b}$. <br>`\n texteCorr += 'We can then read the leading coefficient $a$ of the line $(d)$.<br>'\n texteCorr += 'We know that $a=\\\\dfrac{\\\\text{Vertical displacement}}{\\\\text{Horizontal displacement}}$'\n texteCorr += `<br>By reading the vertical displacement corresponding to a horizontal displacement of one unit, we read: <br>$a=\\\\dfrac{\\\\text{Vertical difference}}{1}=${a}$`\n texteCorr += '<br>We can deduce that the reduced equation of the line $(d)$ is:'\n\n texteCorr += `$y=${reduireAxPlusB(a, b)}$`\n }\n if (b + a < -5 || b + a > 5) {\n s1 = segment(-2, b - 2 * a, -1, b - 2 * a, 'blue')\n s2 = segment(-1, b - 2 * a, -1, b - a, 'blue')\n o = texteParPosition('O', -0.5, -0.5, 'medium', 'black', 1)\n s1.epaisseur = 4\n s2.epaisseur = 4\n const A = point(0, b, 'A')\n t = tracePoint(A, 'blue') // Variable qui trace les points avec une croix\n l = labelPoint(A, 'blue')// Variable qui trace les nom s A et B\n if (a !== 0) {\n texteCorr += mathalea2d({\n xmin: -8,\n ymin: -8,\n xmax: 8,\n ymax: 8,\n scale: 0.5\n }, r, s1, s2, t, l, c, o)\n }\n } else {\n s1 = segment(0, b, 1, b, 'blue')\n s2 = segment(1, b, 1, b + a, 'blue')\n o = texteParPosition('O', -0.5, -0.5, 'medium', 'black', 1)\n s1.epaisseur = 4\n s2.epaisseur = 4\n const A = point(0, b, 'A')\n t = tracePoint(A, 'blue') // Variable qui trace les points avec une croix\n l = labelPoint(A, 'blue')// Variable qui trace les nom s A et B\n if (a !== 0) {\n texteCorr += mathalea2d({\n xmin: -8,\n ymin: -8,\n xmax: 8,\n ymax: 8,\n scale: 0.5\n }, r, s1, s2, t, l, c, o)\n }\n }\n // We draw the graph\n setReponse(this, i, 'y=' + reduireAxPlusB(a, b))\n if (context.isAmc) {\n this.autoCorrection[i] = {\n enonce: texte + '<br>',\n propositions: [\n {\n type: 'AMCNum',\n propositions: [{\n texte: texteCorr,\n statut: '',\n reponse: {\n texte: 'leading coefficient',\n valeur: a,\n param: {\n digits: 1,\n decimals: 0,\n signe: true,\n approx: 0\n }\n }\n }]\n },\n {\n type: 'AMCNum',\n propositions: [{\n statut: '',\n reponse: {\n texte: 'originally ordered',\n valeur: b,\n param: {\n digits: 1,\n decimals: 0,\n signe: true,\n approx: 0\n }\n }\n }]\n }\n ]\n }\n }\n } else { // cas du coeff directeur fractionnaire\n a = randint(-5, 5, [0]) // numérateur coefficient directeur non nul\n b = randint(-5, 5) // ordonnée à l'origine\n d = randint(2, 5, 3) // dénominateur coefficient directeur\n if (a === 0 && b === 0) {\n a = 1\n d = 3\n }// On évite la situation de double nullité\n\n r = repere({\n xMin: -6,\n xMax: 6,\n yMin: -6,\n yMax: 6,\n yLabelEcart: 0.8,\n yLabelDistance: 2,\n xLabelDistance: 2,\n grilleX: false,\n grilleY: false,\n grilleSecondaire: true,\n grilleSecondaireYDistance: 1,\n grilleSecondaireXDistance: 1,\n grilleSecondaireYMin: -6,\n grilleSecondaireYMax: 6,\n grilleSecondaireXMin: -6,\n grilleSecondaireXMax: 6\n })\n c = droite(a / d, -1, b) // On définit l'objet qui tracera la courbe dans le repère\n c.color = 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texteCorr += `We read here that: $A(0,${b}) \\\\in (d)$.<br>`\n texteCorr += `We can then conclude that the intercept is: $b=${b}$. <br>`\n texteCorr += 'We can then read the leading coefficient $a$ of the line $(d)$.<br>'\n texteCorr += 'We know that $a=\\\\dfrac{\\\\text{Vertical displacement}}{\\\\text{Horizontal displacement}}$'\n texteCorr += '<br>We are looking for a horizontal displacement corresponding to an entire vertical displacement.'\n texteCorr += `<br>We read that for a movement to the right of ${d} units, it is necessary`\n\n if (a > 0) {\n texteCorr += 'rise from'\n }\n if (a < 0) {\n texteCorr += 'come down from'\n }\n texteCorr += `${abs(a)} units. `\n texteCorr += `<br>He comes: $a=\\\\dfrac{${a}}{${d}}`\n if (pgcd(a, d) !== 1) {\n texteCorr += `=${texFractionReduite(a, d)}`\n }\n texteCorr += '$'\n\n texteCorr += '<br>We can deduce that the reduced equation of the line $(d)$ is: $y='\n if (a === d) {\n texteCorr += `x${b !== 0 ? ecritureAlgebrique(b) : ''}`\n } 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