// Numbas version: finer_feedback_settings
{"name": "Hallar la ecuaci\u00f3n de una recta perpendicular a otra", "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 perpendicular a otra", "tags": [], "metadata": {"description": "<p>Encuentre la ecuaci&oacute;n de recta perpendicular a una recta dada&nbsp; que pasa por el punto $ (a, b) $.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Encuentra la ecuaci&oacute;n de la recta que:</p>\n<ul>\n<li>Es perpendicular a:&nbsp; &nbsp; &nbsp;$\\displaystyle \\simplify{{(b-d)/n2} x + {(c-a) /n2} y = {(b*c-a*d) / n2}} $ y que pasa por el punto $ (\\var{h}, \\var{k}) $.<br/>&nbsp;</li>\n</ul>\n<p>Ingrese su respuesta en la forma $mx + c$ para los valores adecuados de $ m $ y $ c $.</p>\n<p>Indicaci&oacute;n.</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 si necesita ayuda.</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;&nbsp; $\\dfrac{-1}{n}$ donde $n$ es la pendiente de la recta $\\displaystyle \\simplify{{(b-d)/n2}x+{(c-a)/n2}y={(b*c-a*d)/n2}}$, donde&nbsp; $\\displaystyle n= \\simplify{{b-d}/{a-c}}$. Habiendo calculado $n$, calculamos $\\displaystyle m=\\dfrac{-1}{n} = \\simplify{{a-c}/{d-b}}$. Podemos calcular el t&eacute;rmino constante&nbsp; $c$ notando que $y=\\var{k}$ when $x=\\var{h}$.</p>\n<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-footer-wrap source-or-target-footer\">\n<div class=\"character-count tlid-character-count\">\n<div class=\"cc-ctr normal\"></div>\n</div>\n<div class=\"source-footer\">\n<div class=\"speech-wrap source-or-target-footer-button left-positioned\"></div>\n<div class=\"src-tts left-positioned ttsbutton jfk-button-flat source-or-target-footer-button jfk-button\" aria-label=\"Escuchar\" data-tooltip=\"Escuchar\" aria-pressed=\"false\" role=\"button\" data-tooltip-align=\"t,c\" aria-hidden=\"false\" aria-disabled=\"false\" tabindex=\"0\">\n<div class=\"jfk-button-img\">Usando esto obtenemos:</div>\n</div>\n</div>\n</div>\n</div>\n</div>\n</div>\n</div>\n<p>\\[ \\begin{eqnarray} \\var{k}&amp;=&amp;\\simplify[std]{({a-c}/{d-b}){h}+c} \\Rightarrow\\\\ c&amp;=&amp;\\simplify[std]{{k}-({a-c}/{d-b}){h}={c*h-a*h+d*k-b*k}/{d-b}} \\end{eqnarray} \\]</p>\n<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 class=\"source-footer-wrap source-or-target-footer\">\n<div class=\"character-count tlid-character-count\"></div>\n<div class=\"source-footer\">\n<div class=\"speech-wrap source-or-target-footer-button left-positioned\">\n<div id=\"gt-speech\" class=\"speech-button goog-toolbar-button\" aria-label=\"Activar la entrada de voz\" data-tooltip-align=\"t,c\" aria-pressed=\"false\" role=\"button\" aria-disabled=\"false\" data-tooltip=\"Activar la entrada de voz\" tabindex=\"0\"></div>\n</div>\n</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=\"\">De ah&iacute; que la ecuaci&oacute;n de la recta sea</span></span></div>\n</div>\n</div>\n</div>\n</div>\n<p>\\[y = \\simplify[std]{({a-c}/{d-b})x+{c*h-a*h+d*k-b*k}/{d-b}}\\]</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "(b*c-a*d)/(c-a)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(d1..11)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "a+Random(1..4)*s1", "description": "", "templateType": "anything"}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "d+1", "description": "", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1,-1)*random(1..4)", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "(b-d)/(a-c)", "description": "", "templateType": "anything"}, "n1": {"name": "n1", "group": "Ungrouped variables", "definition": "gcd(b-d,c-a)", "description": "", "templateType": "anything"}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(-1,1)", "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"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "h", "s1", "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 l&iacute;nea es de la forma $ y = mx + c $.<br/>La pendiente $ m $ ser&aacute; el $\\dfrac {-1} {n}$ donde $n$ es la pendiente de la recta $ \\displaystyle \\simplify {{(b*d) / n2} x + {(c*a) / n2} y = {(b * c*a * d) / n2}} $, as&iacute; que podemos comenzar calcular la pendiente de la segunda recta. Habiendo calculado $n$, calcule $ m = \\dfrac {-1} {n} $ y finalmente calcule el t&eacute;rmino constante $c$ 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": "({a-c}/{d-b})x+{c*h-a*h+d*k-b*k}/{d-b}", "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", "type": "question", "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/"}]}