// Numbas version: finer_feedback_settings
{"name": "Julie's copy of Q3 Given 2 lines, Coordinate Geometry 1", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"inter": {"definition": "\n      var a = Numbas.jme.unwrapValue(scope.variables.p_m);\n      var b = Numbas.jme.unwrapValue(scope.variables.p_c);\n      var c = Numbas.jme.unwrapValue(scope.variables.r_m);\n      var d = Numbas.jme.unwrapValue(scope.variables.r_c);\n\n      var miny = Numbas.jme.unwrapValue(scope.variables.miny);\n         var maxy = Numbas.jme.unwrapValue(scope.variables.maxy);\n        var minx = Numbas.jme.unwrapValue(scope.variables.minx);\n         var maxx = Numbas.jme.unwrapValue(scope.variables.maxx);\n        var div = Numbas.extensions.jsxgraph.makeBoard('600px','600px',\n      {boundingBox:[minx,maxy,maxx,miny],\n       axis:true,\n       showNavigation:false,\n       grid:true});\n        var brd = div.board;  \n        var li1=brd.create('line',[[0,-b],[1,a-b]],{fixed:true,name:'Line P',withLabel:true});\n        var li2=brd.create('line',[[0,d],[1,c+d]],{fixed:true,name:'Line R',withLabel:true});\n        \n\n        return div;\n      ", "type": "html", "language": "javascript", "parameters": []}}, "ungrouped_variables": ["pr", "c1", "c2", "a", "b", "val1", "above1", "below1", "on1", "mark1a", "mark1b", "mark1o", "val2", "above2", "below2", "on2", "mark2a", "mark2b", "mark2o"], "name": "Julie's copy of Q3 Given 2 lines, Coordinate Geometry 1", "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>P&nbsp;=&gt; 3x - 2y -6 = 0 and&nbsp;R&nbsp;=&gt; 2x + 3y -35 = 0</p>\n<p>a)&nbsp;point a(4,-2) on, above or below P</p>\n<p>P&nbsp;=&gt; &nbsp;y = $\\frac{3}{2}$x&nbsp;- 3</p>\n<p>$\\frac{3}{2}$(4) - 3 = 3</p>\n<p>-2 &lt; 3</p>\n<p>=&gt; point a is below P</p>\n<p>b) point b(16,1) on, above or below&nbsp;R</p>\n<p>R&nbsp;=&gt; &nbsp;y = -$\\frac{2}{3}$x +&nbsp;$\\frac{35}{3}$</p>\n<p>-$\\frac{2}{3}$(16) +&nbsp;$\\frac{35}{3}$&nbsp;=&nbsp;1</p>\n<p>1&nbsp;=&nbsp;1</p>\n<p>=&gt; point b is on R</p>\n<p>c) Find&nbsp;the slope of P&nbsp;and the slope of R.</p>\n<p>slope of P&nbsp;(m1)&nbsp;= $ \\frac{3}{2}$</p>\n<p>slope of R (m2)&nbsp;= $ -\\frac{2}{3}$</p>\n<p>$ \\frac{3}{2} \\times &nbsp;-\\frac{2}{3}$ = -1&nbsp;</p>\n<p>=&gt; P is perpendicular to R</p>\n<p>d)&nbsp;</p>\n<p>3x - 2y -6 = 0 &nbsp; &nbsp; (X 3) =&gt;&nbsp;9x - 6y =&nbsp;18</p>\n<p>2x + 3y -35 = 0 &nbsp;(X 2) =&gt;&nbsp;4x +&nbsp;6y =&nbsp;70</p>\n<p>=&gt; 13x = 88&nbsp;</p>\n<p>x =&nbsp;6.77</p>\n<p>3(6.77) - 2y -6 = 0</p>\n<p>y = 7.16</p>\n<p>point of intersection = (6.77 , 7.16)</p>\n<p>e) x-axis intersect of P</p>\n<p>y=0 =&gt;&nbsp;3x - 2(0) -6 = 0 =&gt; x = 2</p>\n<p>point = (2 , 0)</p>\n<p>y-axis intersect of P</p>\n<p>x=0 =&gt;&nbsp;3(0) - 2y -6 = 0 =&gt; y&nbsp;=&nbsp;-3</p>\n<p>point = (0 , -3)</p>\n<p>f) $(\\frac{4+16}{2},\\frac{-2+1}{2}) = (10,-\\frac{1}{2})$</p>\n<p>g)&nbsp;Using the formula dis = $\\sqrt((X2-X1)^2 + (Y2-Y1)^2)$,&nbsp;where&nbsp;(X1,Y1) = b(16,1)&nbsp;and&nbsp;(X2,Y2) = a(4,-2).</p>\n<p>$\\sqrt((4-16)^2 + (-2-1)^2)$</p>\n<p>$\\sqrt(144 + 9) = 12.37$</p>\n<p>h) Point (a,2) is on R</p>\n<p>2x + 3y -35 = 0</p>\n<p>2(a) + 3(2) -35 = 0</p>\n<p>2a = 29</p>\n<p>a = 14.5</p>\n<p>i) Line parallel to R contains (-2,5) and (p,4)</p>\n<p>$\\frac{4-5}{p-(-2)} = -\\frac{2}{3}$</p>\n<p>$p = -\\frac{1}{2}$</p>", "rulesets": {}, "parts": [{"prompt": "<p>Is the point a($\\var{a[0]}$,$\\var{a[1]}$) on, above or below the line P?</p>", "matrix": "mark1a", "shuffleChoices": true, "variableReplacements": [], "choices": ["<p>Above</p>", "<p>Below</p>", "<p>On</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "marks": 0, "scripts": {}, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "<p>Is the point b($\\var{b[0]}$,$\\var{b[1]}$) on, above or below the line R?</p>", "matrix": "mark2a", "shuffleChoices": true, "variableReplacements": [], "choices": ["<p>Above</p>", "<p>Below</p>", "<p>On</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "marks": 0, "scripts": {}, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "<p>Give answer in fraction form.</p>\n<p>Find the slope of line P:</p>\n<p>[[0]]</p>\n<p>Find the slope of line R:</p>\n<p>[[1]]</p>\n<p>Is P perpendicular to R.</p>\n<p>[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{pr[0]}/{pr[1]}", "minValue": "{pr[0]}/{pr[1]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}, {"allowFractions": true, "variableReplacements": [], "maxValue": "-{pr[1]}/{pr[0]}", "minValue": "-{pr[1]}/{pr[0]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "yes", "marks": 0, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Find the point of intersection&nbsp;of P and R.</p>\n<p>Give answer to 2 decimal places.</p>\n<p>([[0]],[[1]])</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{x4}+0.01", "minValue": "{x4}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{y4}+0.01", "minValue": "{y4}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Find the&nbsp;points, c and d, where R intersects both axes.</p>\n<p>Give answer in fraction form.</p>\n<p>Point c, R&nbsp;intersects x-axis = ([[0]],[[1]])</p>\n<p>Point d, R&nbsp;intersects y-axis = ([[2]],[[3]])</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{c2}/{pr[1]}+0.01", "minValue": "{c2}/{pr[1]}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "0", "minValue": "0", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}, {"allowFractions": true, "variableReplacements": [], "maxValue": "0", "minValue": "0", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": true, "variableReplacements": [], "precision": 0, "showPrecisionHint": true, "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "100", "scripts": {}, "marks": 1, "maxValue": "{c2}/{pr[0]}+0.01", "minValue": "{c2}/{pr[0]}-0.01", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Find the mid-point of the line segment ab.</p>\n<p>Give answer to 2 decimal points.</p>\n<p>([[0]],[[1]])</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{x5}", "minValue": "{x5}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{y5}", "minValue": "{y5}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Calculate the distance from b&nbsp;to a.</p>\n<p>Give answer to 2 decimal places.</p>\n<p>ans = [[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": true, "variableReplacements": [], "precision": "2", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "maxValue": "{dis}+0.1", "minValue": "{dis}-0.1", "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>The point (a , $\\var{n6}$) is on &nbsp;P, find the value of a.</p>\n<p>Give answer to 2 decimal places.</p>\n<p>a =&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans7}+0.01", "minValue": "{ans7}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>The line containing ($\\var{neg8}$ , $\\var{pos8[0]}$) and (p , $\\var{pos8[1]}$) is parallel to R. Evaluate p. Give your answer correct to two decimal places.</p>\n<p>p =&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans8}+0.01", "minValue": "{ans8}-0.01", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": ["jsxgraph"], "statement": "<p>{inter()}</p>\n<p>P is the line $\\var{pr[0]}x - \\var{pr[1]}y - \\var{c1} = 0$&nbsp;and R&nbsp;is the line $\\var{pr[1]}x + \\var{pr[0]}y - \\var{c2} = 0$.</p>\n<p></p>\n<p></p>", "variable_groups": [{"variables": ["x4", "y4"], "name": "iv"}, {"variables": ["m_p", "m_r", "perp", "mark3"], "name": "iii"}, {"variables": ["x5", "y5", "cx", "dy"], "name": "v and vi"}, {"variables": ["dis", "n6", "ans7"], "name": "vii"}, {"variables": ["neg8", "pos8", "ans8"], "name": "viii"}, {"variables": ["p_m", "p_c", "r_m", "r_c", "minx", "maxx", "miny", "maxy"], "name": "graph"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans8": {"definition": "((pos8[1]-pos8[0])/m_r)+neg8", "templateType": "anything", "group": "viii", "name": "ans8", "description": ""}, "p_m": {"definition": "precround(pr[0]/pr[1],2)", "templateType": "anything", "group": "graph", "name": "p_m", "description": ""}, "p_c": {"definition": "precround(c1/pr[1],2)", "templateType": "anything", "group": "graph", "name": "p_c", "description": ""}, "ans7": {"definition": "(c1+(pr[1]*n6))/pr[0]", "templateType": "anything", "group": "vii", "name": "ans7", "description": ""}, "minx": {"definition": "min(0,ceil((r_c-p_c)/(p_m-r_m))-5)", "templateType": "anything", "group": "graph", "name": "minx", "description": ""}, "below2": {"definition": "if(b[1] < val2,true,false)", "templateType": "anything", "group": "Ungrouped variables", "name": "below2", "description": ""}, "below1": {"definition": "if(a[1] < val1,true,false)", "templateType": "anything", "group": "Ungrouped variables", "name": "below1", "description": ""}, "cx": {"definition": "c2/pr[0]", "templateType": "anything", "group": "v and vi", "name": "cx", "description": ""}, "pos8": {"definition": "shuffle(3..7)[0..2]", "templateType": "anything", "group": "viii", "name": "pos8", "description": ""}, "val2": {"definition": "((-pr[1]/pr[0])*b[0])+((c2/pr[0]))", "templateType": "anything", "group": "Ungrouped variables", "name": "val2", "description": ""}, "val1": {"definition": "((pr[0]/pr[1])*a[0])-((c1/pr[1]))", "templateType": "anything", "group": "Ungrouped variables", "name": "val1", "description": ""}, "y5": {"definition": "(a[1]+b[1])/2", "templateType": "anything", "group": "v and vi", "name": "y5", "description": ""}, "y4": {"definition": "((pr[0]*c2) - (pr[1]*c1))/((pr[0]*pr[0])+(pr[1]*pr[1]))", "templateType": "anything", "group": "iv", "name": "y4", "description": ""}, "pr": {"definition": "shuffle(2..5 except 4)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "pr", "description": ""}, "maxx": {"definition": "max(0,ceil((r_c-p_c)/(p_m-r_m))+5)", "templateType": "anything", "group": "graph", "name": "maxx", "description": ""}, "maxy": {"definition": "max(0,ceil((p_m*r_c-p_c*r_m)/(p_m-r_m))+5)", "templateType": "anything", "group": "graph", "name": "maxy", "description": ""}, "perp": {"definition": "if(m_p*m_r = -1,true,false)", "templateType": "anything", "group": "iii", "name": "perp", "description": ""}, "mark1b": {"definition": "[if(below1=true,1,0),if(below1=true,0,1)]", "templateType": "anything", "group": "Ungrouped variables", "name": "mark1b", "description": ""}, "r_m": {"definition": "precround(-pr[1]/pr[0],2)", "templateType": "anything", "group": "graph", "name": "r_m", "description": ""}, "mark1a": {"definition": "[if(above1=true,1,0),if(below1=true,1,0),if(below1=true,1,0)]", "templateType": "anything", "group": "Ungrouped variables", "name": "mark1a", "description": ""}, "mark1o": {"definition": "[if(on1=true,1,0),if(on1=true,0,1)]", "templateType": "anything", "group": "Ungrouped variables", "name": "mark1o", "description": ""}, "r_c": {"definition": "precround(c2/pr[0],2)", "templateType": "anything", "group": "graph", "name": "r_c", "description": ""}, "neg8": {"definition": "random(-6..-2)", "templateType": "anything", "group": "viii", "name": "neg8", "description": ""}, "dy": {"definition": "c2/pr[1]", "templateType": "anything", "group": "v and vi", "name": "dy", "description": ""}, "on2": {"definition": "if(b[1] = val2,true,false)", "templateType": "anything", "group": "Ungrouped variables", "name": "on2", "description": ""}, "c2": {"definition": "random(25..39)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "c1": {"definition": "random(5..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "on1": {"definition": "if(a[1] = val1,true,false)", "templateType": "anything", "group": "Ungrouped variables", "name": "on1", "description": ""}, "x4": {"definition": "((pr[1]*c2) + (pr[0]*c1))/((pr[0]*pr[0])+(pr[1]*pr[1]))", "templateType": "anything", "group": "iv", "name": "x4", "description": ""}, "x5": {"definition": "(a[0]+b[0])/2", "templateType": "anything", "group": "v and vi", "name": "x5", "description": ""}, "a": {"definition": "shuffle(2..5)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "shuffle(7..15)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "miny": {"definition": "min(0,ceil((p_m*r_c-p_c*r_m)/(p_m-r_m))-5)", "templateType": "anything", "group": "graph", "name": "miny", "description": ""}, "above2": {"definition": "if(b[1] > val2,true,false)", "templateType": "anything", "group": "Ungrouped variables", "name": "above2", "description": ""}, "above1": {"definition": "if(a[1] > val1,true,false)", "templateType": "anything", "group": "Ungrouped variables", "name": "above1", "description": ""}, "mark2o": {"definition": "[if(on2=true,1,0),if(on2=true,0,1)]", "templateType": "anything", "group": "Ungrouped variables", "name": "mark2o", "description": ""}, "n6": {"definition": "random(2..6)", "templateType": "anything", "group": "vii", "name": "n6", "description": ""}, "mark3": {"definition": "[if(perp=true,1,0),if(perp=true,0,1)]", "templateType": "anything", "group": "iii", "name": "mark3", "description": ""}, "m_r": {"definition": "-precround((pr[1]/pr[0]),2)", "templateType": "anything", "group": "iii", "name": "m_r", "description": ""}, "m_p": {"definition": "pr[0]/pr[1]", "templateType": "anything", "group": "iii", "name": "m_p", "description": ""}, "mark2b": {"definition": "[if(below2=true,1,0),if(below2=true,0,1)]", "templateType": "anything", "group": "Ungrouped variables", "name": "mark2b", "description": ""}, "mark2a": {"definition": "[if(above2=true,1,0),if(above2=true,1,0),if(below2=true,1,0)]", "templateType": "anything", "group": "Ungrouped variables", "name": "mark2a", "description": ""}, "dis": {"definition": "sqrt(((a[1]-b[1])^2) + ((a[0]-b[0])^2))", "templateType": "anything", "group": "vii", "name": "dis", "description": ""}}, "metadata": {"description": "<p>Reading information from the equation of the line. Graph shown</p>\n<p>Rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}