// Numbas version: exam_results_page_options
{"name": "Hallar la ecuaci\u00f3n de una recta paralela a una recta dada...", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Hallar la ecuaci\u00f3n de una recta paralela a una recta dada...", "tags": [], "metadata": {"description": "<p>Encuentre la ecuaci&oacute;n de la l&iacute;nea recta paralela a la recta que pasa por el punto $ (a, b) $.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<div class=\"tlid-input input\">\n<div class=\"source-wrap\">\n<div class=\"input-full-height-wrapper tlid-input-full-height-wrapper\">\n<div class=\"source-input\">\n<div class=\"source-header\">\n<div class=\"go-wrap\"></div>\n</div>\n</div>\n</div>\n</div>\n</div>\n<div class=\"tlid-results-container results-container\">\n<div class=\"tlid-result result-dict-wrapper\">\n<div class=\"result tlid-copy-target\">\n<div class=\"text-wrap tlid-copy-target\">\n<div class=\"result-shield-container tlid-copy-target\"><span class=\"tlid-translation translation\"><span title=\"\" class=\"\"></span></span></div>\n<div class=\"result-shield-container tlid-copy-target\"><span class=\"tlid-translation translation\"><span title=\"\" class=\"\">Encuentra la ecuaci&oacute;n de la recta que:</span></span></div>\n</div>\n</div>\n</div>\n</div>\n<ul>\n<li>Es paralela a la recta L: $\\displaystyle \\simplify{{(b-d)/n2}x+{(c-a)/n2}y={(b*c-a*d)/n2}}$ y que pasa por el punto $A(\\var{h},\\var{k})$.</li>\n</ul>\n<p>&nbsp;Ingrese su respuesta en la forma $ mx + c $ para los valores adecuados de $ m $ y $ c $.</p>\n<p></p>\n<p><strong><em>Indicaci&oacute;n</em></strong></p>\n<p>Ingrese $m$ y $c$ como fracciones o enteros seg&uacute;n sea apropiado y no como decimales.</p>\n<p>Si ingresa $m$ como fracci&oacute;n, ponga corchetes () alrededor de la fracci&oacute;n. Por ejemplo, si su respuesta para $m$ es $\\dfrac{-2} {3} $ y su respuesta para $ c $ es $\\dfrac{7}{5} $, debe escribir $ (- 2/3)x + 7/5 $.</p>\n<p>Haga clic en Mostrar pasos (shows steps) si necesita ayuda.</p>\n<p></p>", "advice": "<p>La ecuaci&oacute;n de la recta es de la forma. $y=mx+c$.</p>\n<p>La pendiente $m$ ser&aacute; la misma que la pendiente de la recta $\\displaystyle \\simplify{{(b-d)/n2}x+{(c-a)/n2}y={(b*c-a*d)/n2}}$, donde $\\displaystyle m= \\simplify{{b-d}/{a-c}}$. Podemos calcular el t&eacute;rmino constante $c$ observando que $y=\\var{k}$ donde $x=\\var{h}$.</p>\n<p>Usando esto obtenemos:<br/>\\[ \\begin{eqnarray} \\var{k}&amp;=&amp;\\simplify[std]{({b-d}/{a-c}){h}+c} \\Rightarrow\\\\ c&amp;=&amp;\\simplify[std]{{k}-({b-d}/{a-c}){h}={(b*h-d*h+c*k-a*k)}/{(c-a)}} \\end{eqnarray} \\]</p>\n<p>De ah&iacute; que la ecuaci&oacute;n de la recta sea:<br/>\\[y = \\simplify[std]{({b-d}/{a-c})x+{b*h-d*h+c*k-a*k}/{c-a}}\\]</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1,-1)*random(1..4)", "description": "", "templateType": "anything"}, "n2": {"name": "n2", "group": "Ungrouped variables", "definition": "if(b*c=a*d,1,gcd(n1,b*c-a*d))", "description": "", "templateType": "anything"}, "k1": {"name": "k1", "group": "Ungrouped variables", "definition": "(b*c-a*d-b*h+d*h)/(c-a)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "a+Random(1..4)*s1", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "(b-d)/(a-c)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(d1..11)", "description": "", "templateType": "anything"}, "n1": {"name": "n1", "group": "Ungrouped variables", "definition": "gcd(b-d,c-a)", "description": "", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(-9..9 except k1)", "description": "", "templateType": "anything"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "(b*c-a*d)/(c-a)", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything"}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "d+1", "description": "", "templateType": "anything"}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "h", "s1", "k1", "n1", "n2", "k", "d1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$y=\\;\\phantom{{}}$[[0]]</p>", "stepsPenalty": 1, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>La ecuaci&oacute;n de la recta es de la forma $y= mx+c$.</p>\n<p>La pendiente $m$&nbsp;ser&aacute; la misma que la pendiente de la recta. $\\displaystyle \\simplify{{(b-d)/n2}x+{(c-a)/n2}y={(b*c-a*d)/n2}}$,</p>\n<p>Puedes empezar por calcular la pendiente de la segunda recta. Habiendo calculado $ m $, calcule el t&eacute;rmino de la constante $c$&nbsp; observando que $ y=\\var{k} $ cuando $x=\\var{h}$.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 2, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({b-d}/{a-c})x+{b*h-d*h+c*k-a*k}/{c-a}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": "<p>Input all numbers as fractions or integers as appropriate and not as decimals.</p>"}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}