// Numbas version: exam_results_page_options {"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 => 3x - 2y -6 = 0 and R => 2x + 3y -35 = 0

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a) point a(4,-2) on, above or below P

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P =>  y = $\\frac{3}{2}$x - 3

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$\\frac{3}{2}$(4) - 3 = 3

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-2 < 3

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=> point a is below P

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b) point b(16,1) on, above or below R

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R =>  y = -$\\frac{2}{3}$x + $\\frac{35}{3}$

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-$\\frac{2}{3}$(16) + $\\frac{35}{3}$ = 1

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1 = 1

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=> point b is on R

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c) Find the slope of P and the slope of R.

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slope of P (m1) = $ \\frac{3}{2}$

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slope of R (m2) = $ -\\frac{2}{3}$

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$ \\frac{3}{2} \\times  -\\frac{2}{3}$ = -1 

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=> P is perpendicular to R

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d) 

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3x - 2y -6 = 0     (X 3) => 9x - 6y = 18

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2x + 3y -35 = 0  (X 2) => 4x + 6y = 70

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=> 13x = 88 

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x = 6.77

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3(6.77) - 2y -6 = 0

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y = 7.16

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point of intersection = (6.77 , 7.16)

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e) x-axis intersect of P

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y=0 => 3x - 2(0) -6 = 0 => x = 2

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point = (2 , 0)

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y-axis intersect of P

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x=0 => 3(0) - 2y -6 = 0 => y = -3

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point = (0 , -3)

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f) $(\\frac{4+16}{2},\\frac{-2+1}{2}) = (10,-\\frac{1}{2})$

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g) Using the formula dis = $\\sqrt((X2-X1)^2 + (Y2-Y1)^2)$, where (X1,Y1) = b(16,1) and (X2,Y2) = a(4,-2).

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$\\sqrt((4-16)^2 + (-2-1)^2)$

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$\\sqrt(144 + 9) = 12.37$

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h) Point (a,2) is on R

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2x + 3y -35 = 0

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2(a) + 3(2) -35 = 0

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2a = 29

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a = 14.5

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i) Line parallel to R contains (-2,5) and (p,4)

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$\\frac{4-5}{p-(-2)} = -\\frac{2}{3}$

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$p = -\\frac{1}{2}$

", "rulesets": {}, "parts": [{"prompt": "

Is the point a($\\var{a[0]}$,$\\var{a[1]}$) on, above or below the line P?

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Above

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Below

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On

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Is the point b($\\var{b[0]}$,$\\var{b[1]}$) on, above or below the line R?

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On

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Give answer in fraction form.

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Find the slope of line P:

\n

[[0]]

\n

Find the slope of line R:

\n

[[1]]

\n

Is P perpendicular to R.

\n

[[2]]

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Find the point of intersection of P and R.

\n

Give answer to 2 decimal places.

\n

([[0]],[[1]])

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Find the points, c and d, where R intersects both axes.

\n

Give answer in fraction form.

\n

Point c, R intersects x-axis = ([[0]],[[1]])

\n

Point d, R intersects y-axis = ([[2]],[[3]])

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Find the mid-point of the line segment ab.

\n

Give answer to 2 decimal points.

\n

([[0]],[[1]])

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Calculate the distance from b to a.

\n

Give answer to 2 decimal places.

\n

ans = [[0]]

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The point (a , $\\var{n6}$) is on  P, find the value of a.

\n

Give answer to 2 decimal places.

\n

a = [[0]]

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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.

\n

p = [[0]]

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{inter()}

\n

P is the line $\\var{pr[0]}x - \\var{pr[1]}y - \\var{c1} = 0$ and R is the line $\\var{pr[1]}x + \\var{pr[0]}y - \\var{c2} = 0$.

\n

\n

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Reading information from the equation of the line. Graph shown

\n

Rebelmaths

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