// Numbas version: finer_feedback_settings
{"name": "Vectors: Finding Coordinates 1", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vectors: Finding Coordinates 1", "tags": [], "metadata": {"description": "<p>Given the position vectors of three 2-dimensional points $A$, $B$ and $C$, find the coordinates of a fourth point $D$ such that $ABCD$ forms a parallelogram.&nbsp;</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>There are 3 points $A$, $B$, $C$, with position vectors \\[ \\mathbf a = \\var{a},\\quad \\mathbf b = \\var{b},\\quad \\mathbf c= \\var{c} \\]</p>\n<p>respectively.</p>\n<p>Find the coordinates of the point $D$ such that $ABCD$ forms a parallelogram.</p>", "advice": "<p>We want to find the position vector $\\mathbf d = \\vec{OD}$, such that $ABCD$ forms a parallelogram.</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/jqaptsj6',defs)}</p>\n<p>For $ABCD$ to be a parallelogram, then $\\vec{AB} = \\vec{DC}$. In terms of the points' position vectors,</p>\n<p>\\[ \\begin{split} \\vec{AB} &amp;\\,= \\mathbf b - \\mathbf a &amp;\\,= \\var{b-a} ,\\\\\\\\ \\vec{DC} &amp;\\,= \\mathbf c - \\mathbf d &amp;\\,= \\var{c} - \\mathbf d. \\end{split} \\]</p>\n<p>Therefore, \\[ \\begin{split} \\var{b-a} &amp;\\,= \\var{c} -\\mathbf d \\\\ \\implies \\mathbf d &amp;\\,= \\var{c+a-b}. \\end{split}\\]</p>\n<p>Hence, the co-ordinates of $D$ are $(\\var{d[0]},\\var{d[1]})$.</p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "vector(random(-4..-2),random(-1..-2))", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "vector(1,random(3..5))", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "vector(random(4..6),random(3..4))", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "a+c-b", "description": "", "templateType": "anything", "can_override": false}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['A',a],\n  ['B',b],\n  ['C',c]\n]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "c[0]>b[0]", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "defs"], "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>$D =$ [[0]]</p>", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "matrix([d[0],d[1]])", "correctAnswerFractions": false, "numRows": 1, "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}