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N(A) E Math

PSLE

PSLE Foundation Mathematics

<p>The figure below shows $\Delta ABC$ in the Cartesian plane.</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">On the same grid, mark and label the coordinates of $A$, $B$ and $C$.</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">Find the gradients of the straight lines $AB$, $BC$ and $AC$.</div></li><li data-list-item-id="item-1789466210432-35rhhnif6" data-list-item-path="item-1789466210432-35rhhnif6"><div class="list-item-paragraph"><p>In the same grid, draw the graph of $x = \frac{2}{5}$, for values of $y$ from $-1$ to $2$.</p></div><div class="graph-block" data-graph-config="{"boundingBox":[-6.536,6.2,6.236,-6.2],"width":504,"height":504,"axis":true,"grid":true,"gridSettings":{"majorStepX":1,"majorStepY":1,"minorElementsX":4,"minorElementsY":4,"showMajorGridLines":true,"showMinorGridLines":true,"majorColor":"#A9BFFF","majorOpacity":0.7,"majorStrokeWidth":1.344,"minorColor":"#DCE5FF","minorOpacity":0.8,"minorStrokeWidth":0.672},"keepAspectRatio":true,"showNavigation":false,"showAxisLabels":true,"xTickLabelEvery":1000000,"yTickLabelEvery":1000000,"xAxisLabel":"\\(\\Large x\\)","yAxisLabel":"\\(\\Large y\\)","originLabel":"\\(\\Large 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-5\\)","color":"#000000","fixed":false},{"id":"a26494e4-50d5-47eb-8423-de92b0beb425","type":"text","x":-4.3,"y":-0.4,"label":"\\(\\Large -4\\)","color":"#000000","fixed":false},{"id":"7649804d-b82c-4fc9-8d58-741f207cb5f7","type":"text","x":-3.3,"y":-0.4,"label":"\\(\\Large -3\\)","color":"#000000","fixed":false},{"id":"66e25f43-4d07-4e0f-b933-9dd14557d883","type":"text","x":-2.3,"y":-0.4,"label":"\\(\\Large -2\\)","color":"#000000","fixed":false},{"id":"a4329d85-50ea-41b2-bd6e-f50c7ffc80b0","type":"text","x":-1.3,"y":-0.4,"label":"\\(\\Large -1\\)","color":"#000000","fixed":false},{"id":"ce8e9457-4730-44db-99e4-a14cdc660992","type":"text","x":0.85,"y":-0.4,"label":"\\(\\Large 1\\)","color":"#000000","fixed":false},{"id":"42de1073-60d6-449c-995f-f6e2bbd99ffb","type":"text","x":1.85,"y":-0.4,"label":"\\(\\Large 2\\)","color":"#000000","fixed":false},{"id":"af2965d7-cabe-47b7-b10d-2392d3cccd89","type":"text","x":2.85,"y":-0.4,"label":"\\(\\Large 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The figure below shows $\Delta ABC$ in the Cartesian plane.

On the same grid, mark and label the coordinates of $A$, $B$ and $C$.

Find the gradients of the straight lines $AB$, $BC$ and $AC$.

Gradient of a Straight Line

Plotting of Straight Line on Graph Paper

Basics of Coordinate Geometry

Gradient of Straight Line

Linear Graphs and Its Applications

Coordinate Geometry

<p>A straight line passes through $A \ (0, \frac{8}{5})$ and $B\ (2, 0)$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">In the figure below, mark and label the points $A$ and $B$. Hence draw the line $AB$.</span></div></li><li><div class="list-item-paragraph">Find the gradient and $y$-intercept of the straight line $AB$.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767604178154-rk8kixbia6.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDQxNzgxNTQtcms4a2l4YmlhNi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5ODU2LCJleHAiOjE3OTI3MTAxNTZ9.c8nq3EXcxueZPuvwPZEeFcqLGT_cjWC-Pct2_yWn4qw" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

A straight line passes through $A \ (0, \frac{8}{5})$ and $B\ (2, 0)$.

In the figure below, mark and label the points $A$ and $B$. Hence draw the line $AB$.

Find the gradient and $y$-intercept of the straight line $AB$.

<p>Solve the following graphing and area problems on the provided grid.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">On the grid below, use a scale of $1$ cm as $1$ unit to plot the points $A (2, 5)$, $B (-2, 0)$ and $C (1, 0)$. Hence, find the area of $\Delta ABC$, giving your answers in unit$^2$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Another point $D$ lies on the $x$-axis. Given that the area of $\Delta ACD$ is $5$ unit$^2$, find all the possible coordinates of $D$.</span></div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767602015619-9pqisnoa.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDIwMTU2MTktOXBxaXNub2EucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTg1NiwiZXhwIjoxNzkyNzEwMTU2fQ.RrlypyZQXO0AMv1fIUDBrgF0YzDf7-9bu1RG5-vpERc" style="max-width: min(280px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

Solve the following graphing and area problems on the provided grid.

On the grid below, use a scale of $1$ cm as $1$ unit to plot the points $A (2, 5)$, $B (-2, 0)$ and $C (1, 0)$. Hence, find the area of $\Delta ABC$, giving your answers in unit$^2$.

Another point $D$ lies on the $x$-axis. Given that the area of $\Delta ACD$ is $5$ unit$^2$, find all the possible coordinates of $D$.

Area of Rectilinear Figures

<p>On the grid below, use a scale of $1$ cm as $1$ unit to plot the points $A (0, 5)$, $B (-3, 4)$, $C (-1, -2)$ and $D (2, -1)$, showing clearly the $x$- and $y$- axes and the origin.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767601824822-tm3dglwuia.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDE4MjQ4MjItdG0zZGdsd3VpYS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5ODU2LCJleHAiOjE3OTI3MTAxNTZ9.uTNMDUYRvxwcEOnWbaVG_LHpW-g3M_KQeXY5GFdNRU8" style="max-width: min(280px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

On the grid below, use a scale of $1$ cm as $1$ unit to plot the points $A (0, 5)$, $B (-3, 4)$, $C (-1, -2)$ and $D (2, -1)$, showing clearly the $x$- and $y$- axes and the origin.

<p>Plot each of the following points in the figure below.</p>
<ul class="bullet-list"></ul>
<p>$A (3, 4)$, $B (0, 2)$, $C (-1, 3)$, $D (-3, 0)$, $E (-4, -2)$, $F (0, 5)$, $G (2, -1)$ and $H (4, 1)$.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767601714702-cmrww08pwtv.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDE3MTQ3MDItY21yd3cwOHB3dHYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTg1NiwiZXhwIjoxNzkyNzEwMTU2fQ.KaE6mlPem_ntcPZUnFTK6p38zzEpTLUqRv8xhILmG7w" style="max-width: min(280px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Use a fresh Cartesian grid for the stated coordinates. The retained reference image contains points from a different exercise and must not be used as the answer to this one.</p>
<p>Use this fresh grid for the stated coordinates.</p>
<div class="graph-block" data-graph-config="eyJheGlzIjp0cnVlLCJncmlkIjp0cnVlLCJ3aWR0aCI6NDAwLCJoZWlnaHQiOjM2MCwiYm91bmRpbmdCb3giOlstNyw3LDcsLTddLCJrZWVwQXNwZWN0UmF0aW8iOmZhbHNlLCJzaG93TmF2aWdhdGlvbiI6ZmFsc2UsInNob3dBeGlzTGFiZWxzIjp0cnVlLCJ4QXhpc0xhYmVsIjoieCIsInlBeGlzTGFiZWwiOiJ5IiwiZWxlbWVudHMiOltdLCJncmlkU2V0dGluZ3MiOnsibWFqb3JTdGVwWCI6MSwibWFqb3JTdGVwWSI6MSwic2hvd01ham9yR3JpZExpbmVzIjp0cnVlLCJzaG93TWlub3JHcmlkTGluZXMiOmZhbHNlLCJtYWpvckNvbG9yIjoiIzk0YTNiOCIsIm1ham9yT3BhY2l0eSI6MC40LCJtYWpvclN0cm9rZVdpZHRoIjowLjZ9fQ==" data-width="400" data-height="360" data-proportional style="width:400px;height:360px;max-width:100%;display:flow-root;margin:0 auto;--graph-width:400px;--graph-aspect:400 / 360;"></div>

Plot each of the following points in the figure below.

$A (3, 4)$, $B (0, 2)$, $C (-1, 3)$, $D (-3, 0)$, $E (-4, -2)$, $F (0, 5)$, $G (2, -1)$ and $H (4, 1)$.

Use a fresh Cartesian grid for the stated coordinates. The retained reference image contains points from a different exercise and must not be used as the answer to this one.

Use this fresh grid for the stated coordinates.

<p>Write down the coordinates of each point in the figure below.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767601526918-k82k88x4oes.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDE1MjY5MTgtazgyazg4eDRvZXMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTg1NiwiZXhwIjoxNzkyNzEwMTU2fQ.vP5bI_EMyjiAAcZ2fpWruqNdM72bQQz-F6MQWnWtk_w" style="max-width: min(280px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

Write down the coordinates of each point in the figure below.

 Basics of Coordinate Geometry

<p>The Cartesian plane below shows points $A,B,C,D$ and $E$.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765869583628-vyn7ynvvv7.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU4Njk1ODM2MjgtdnluN3ludnZ2Ny5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5ODU2LCJleHAiOjE3OTI3MTAxNTZ9.tWpbvhQCx3Ai7gDn3A9mElYjTrSCG6f837zvR01psK0" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Write down the coordinates of each point</p>
<ol class="i-list"><li><div class="list-item-paragraph">$A$</div></li><li><div class="list-item-paragraph">$B$</div></li><li><div class="list-item-paragraph">$C$ </div></li><li><div class="list-item-paragraph">$D$</div></li><li><div class="list-item-paragraph">$E$</div></li></ol>

The Cartesian plane below shows points $A,B,C,D$ and $E$.

Writing the Coordinates of a Point

<p>The figure below shows a cartesian plane.</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1765264467497-13jbo9ue3y3.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjUyNjQ0Njc0OTctMTNqYm85dWUzeTMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTg1NiwiZXhwIjoxNzkyNzEwMTU2fQ.js0jdZrxTngSP5Y-hEaxdK9lK8GDOjfqE5ndMtYP7Fk" style="max-width: 400px; height: auto; display: block;" class="aligncenter custom-width" /></figure>
<ol class="abc-list"><li><div class="list-item-paragraph">State the coordinates of the points $A$ and $B$.</div></li><li><div class="list-item-paragraph">Find the gradient of the straight line that join $B$ and $C$.</div></li><li><div class="list-item-paragraph">Plot and label</div><ol class="i-list"><li><div class="list-item-paragraph">point $D$ such that $ABCD$ is a parallelogram.</div></li><li><div class="list-item-paragraph">point $E$ such that $AEBC$ is a parallelogram.</div></li></ol></li><li><div class="list-item-paragraph">Find the area of parallelogram $ABCD$.</div></li></ol>

The figure below shows a cartesian plane.

[EPQ Vol 1A] Question 27

<p>The figure below shows a cartesian plane.</p>
<div class="graph-block" data-graph-config="eyJib3VuZGluZ0JveCI6Wy02LDYsNiwtNl0sIndpZHRoIjo0NTMuNTQzMywiaGVpZ2h0Ijo0NTMuNTQzMywiYXhpcyI6dHJ1ZSwiZ3JpZCI6dHJ1ZSwiZ3JpZFNldHRpbmdzIjp7Im1ham9yU3RlcFgiOjEsIm1ham9yU3RlcFkiOjEsIm1pbm9yRWxlbWVudHNYIjo0LCJtaW5vckVsZW1lbnRzWSI6NCwic2hvd01ham9yR3JpZExpbmVzIjp0cnVlLCJzaG93TWlub3JHcmlkTGluZXMiOnRydWUsIm1ham9yQ29sb3IiOiIjOTRhM2I4IiwibWFqb3JPcGFjaXR5IjowLjU1LCJtYWpvclN0cm9rZVdpZHRoIjowLjgsIm1pbm9yQ29sb3IiOiIjY2JkNWUxIiwibWlub3JPcGFjaXR5IjowLjM1LCJtaW5vclN0cm9rZVdpZHRoIjowLjV9LCJrZWVwQXNwZWN0UmF0aW8iOmZhbHNlLCJzaG93TmF2aWdhdGlvbiI6ZmFsc2UsInNob3dBeGlzTGFiZWxzIjp0cnVlLCJ4VGlja0xhYmVsRXZlcnkiOjEsInlUaWNrTGFiZWxFdmVyeSI6MSwieEF4aXNMYWJlbCI6IlxcKHhcXCkiLCJ5QXhpc0xhYmVsIjoiXFwoeVxcKSIsIm9yaWdpbkxhYmVsIjoiXFwoT1xcKSIsInhBeGlzTGFiZWxPZmZzZXQiOlstNy41LC0xMC4yXSwieUF4aXNMYWJlbE9mZnNldCI6Wy0xMy42LC0yLjJdLCJvcmlnaW5MYWJlbE9mZnNldCI6Wy01LC0yXSwiZWxlbWVudHMiOlt7ImlkIjoiNzA3ZTMwZjItOTFkYS00YjBlLWI3MWItODNiYTUxZTMxMjY1IiwidHlwZSI6InBvaW50IiwieCI6MiwieSI6LTQsImNvbG9yIjoiIzAwMDAwMCIsImxhYmVsIjoiIiwicG9pbnRTaXplIjoxLCJwb2ludFN0eWxlIjoiY2lyY2xlIn0seyJpZCI6IjEwZTYyMzgyLTVmZDItNDAxZi1hYzJhLTU4Yjk1YWQ5ZWFmYiIsInR5cGUiOiJwb2ludCIsIngiOi0zLCJ5IjotMSwiY29sb3IiOiIjMDAwMDAwIiwibGFiZWwiOiIiLCJwb2ludFNpemUiOjEsInBvaW50U3R5bGUiOiJjaXJjbGUifSx7ImlkIjoiNzc2YjZkNzItOTdjYS00YjBhLThmMzctNWVhOGZjZWMwZWQ4IiwidHlwZSI6InBvaW50IiwieCI6MCwieSI6MiwiY29sb3IiOiIjMDAwMDAwIiwibGFiZWwiOiIiLCJwb2ludFNpemUiOjEsInBvaW50U3R5bGUiOiJjaXJjbGUifSx7ImlkIjoiZTkzYTMyODktNzZjZC00ZGE5LWIyOWMtMjBmMmM2OTJhYjViIiwidHlwZSI6InRleHQiLCJ4IjowLCJ5IjowLCJsYWJlbCI6IlxcKFxcKSIsImNvbG9yIjoiIzAwMDAwMCIsInRleHRSb3RhdGlvbiI6MH0seyJpZCI6IjYzMWYzYTlmLTE1YWItNDhkOC05MmNjLWZiNDRmOGI5ZDQ3OSIsInR5cGUiOiJ0ZXh0IiwieCI6LTAuMzksInkiOjIuMTksImxhYmVsIjoiXFwoQVxcKSIsImNvbG9yIjoiIzAwMDAwMCIsInRleHRSb3RhdGlvbiI6MH0seyJpZCI6IjZkN2FhMzBhLWUzYTctNGJmNi04YWNlLTdjYzcwNzA2M2IxNSIsInR5cGUiOiJ0ZXh0IiwieCI6LTMuMzksInkiOi0xLjI4LCJsYWJlbCI6IlxcKEJcXCkiLCJjb2xvciI6IiMwMDAwMDAiLCJ0ZXh0Um90YXRpb24iOjB9LHsiaWQiOiIxNmY3NWFmMy0yOTRlLTRlYmEtODkzYS1jMTMzNDQ2NjAwNDciLCJ0eXBlIjoidGV4dCIsIngiOjIuMDcsInkiOi00LjI4LCJsYWJlbCI6IlxcKENcXCkiLCJjb2xvciI6IiMwMDAwMDAiLCJ0ZXh0Um90YXRpb24iOjB9XSwibWFqb3JTcXVhcmVTaXplTW0iOjEwLCJzaG93WEF4aXMiOnRydWUsInNob3dZQXhpcyI6dHJ1ZSwic2hvd1plcm9UaWNrIjpmYWxzZSwieEF4aXNSYW5nZSI6Wy01LjQ5NDQsNS41ODUyXSwieUF4aXNSYW5nZSI6Wy01LjU1MDUsNS40ODQyXX0=" data-width="453.5433" data-height="453.5433" style="width:120mm;height:120mm;max-width:none;display:flow-root;margin:0 auto;"></div>
<ol class="abc-list"><li data-list-item-id="item-1765264149505-u9tm9cwfv" data-list-item-path="item-1765264149505-u9tm9cwfv"><div class="list-item-paragraph">State the coordinates of the points $A$ and $B$.</div></li><li data-list-item-id="item-1765264150239-rekl7pp2l" data-list-item-path="item-1765264150239-rekl7pp2l"><div class="list-item-paragraph">Find the gradient of the straight line that join $B$ and $C$.</div></li><li data-list-item-id="item-1765264208963-th4p8kh3t" data-list-item-path="item-1765264208963-th4p8kh3t"><div class="list-item-paragraph">Plot and label</div><ol class="i-list"><li data-list-item-id="subitem-1765264215016-dksf61t3e" data-list-item-path="item-1765264208963-th4p8kh3t/subitem-1765264215016-dksf61t3e"><div class="list-item-paragraph">point $D$ such that&nbsp;$ABCD$ is a parallelogram,</div></li><li data-list-item-id="subitem-1765264239466-uqrn2t0ey" data-list-item-path="item-1765264208963-th4p8kh3t/subitem-1765264239466-uqrn2t0ey"><div class="list-item-paragraph">point $E$ such that&nbsp;$AEBC$ is a parallelogram.</div></li></ol></li><li data-list-item-id="item-1765264258824-gg145ek4w" data-list-item-path="item-1765264258824-gg145ek4w"><div class="list-item-paragraph">Find the area of parallelogram $ABCD$.</div></li></ol>

[EPQ Vol 1A] Question 26

<p>Plot each of the following points on the grid below. </p>
<p>$A\left( -1,3 \right)$ , $B\left( 1,-2 \right)$ , $C\left( 3,-2 \right)$ , $D\left( 0,4 \right)$ and $E\left( -5,0 \right)$.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1763740498409-aiq1sbncstd.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjM3NDA0OTg0MDktYWlxMXNibmNzdGQucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTg1NiwiZXhwIjoxNzkyNzEwMTU2fQ.0GtLUogv8g8zBoyrMfU9TG6kWEYKB6I8zK4_JDjcBLw" style="max-width: min(320px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

Plot each of the following points on the grid below. 

$A\left( -1,3 \right)$ , $B\left( 1,-2 \right)$ , $C\left( 3,-2 \right)$ , $D\left( 0,4 \right)$ and $E\left( -5,0 \right)$.

Plotting Points on the Cartesian Coordinate Plane

<p>Plot each of the following points on the grid below.</p>
<p>$A\left( 4,0 \right)$ , $B\left( -6,-4 \right)$ , $C\left( 5,-2 \right)$ , $D\left( 0,-3 \right)$ and $E\left( -2,-5 \right)$.</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1763739643700-namha7bx5kj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjM3Mzk2NDM3MDAtbmFtaGE3Yng1a2oucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTg1NiwiZXhwIjoxNzkyNzEwMTU2fQ.gX3F5e9ackzrAU2HfCuQJO9LM_og0FXRI4Zq33MDUI4" style="max-width: 350px; height: auto; display: block;" class="aligncenter custom-width" /></figure>

Plot each of the following points on the grid below.

$A\left( 4,0 \right)$ , $B\left( -6,-4 \right)$ , $C\left( 5,-2 \right)$ , $D\left( 0,-3 \right)$ and $E\left( -2,-5 \right)$.

Plotting Points on the Cartesian Plane

<p>Write down the coordinates of each of point shown in the figure below.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1763739210355-zf6krn7yqh.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjM3MzkyMTAzNTUtemY2a3JuN3lxaC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5ODU2LCJleHAiOjE3OTI3MTAxNTZ9.CPJ__OaNYQib8dnVnArWeYBMzUTNorgm7l7l_XroRWo" style="max-width: min(350px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

Write down the coordinates of each of point shown in the figure below.

Identifying Coordinates of Points on the Plane

<p>Two points $A$ and $B$ are marked in the Cartesian plane below.</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760434194088-o0tavlfatj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjA0MzQxOTQwODgtbzB0YXZsZmF0ai5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5ODU2LCJleHAiOjE3OTI3MTAxNTZ9.EacuTZqPNFUMclQIQqoGgynNeLnQfRAh_uG5O5G5n4w" style="max-width: 400px; height: auto; display: block;" class="aligncenter custom-width" /></figure>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down the coordinates of $A$ and $B$.</div></li><li><div class="list-item-paragraph">On the graph, plot and label clearly, the point $D\left( 1,-3 \right)$.</div></li><li><div class="list-item-paragraph">Write down the coordinates of the point $C$ such that $ABCD$ is a parallelogram.</div></li><li><div class="list-item-paragraph">Find the area of $ABCD$.</div></li><li><div class="list-item-paragraph">Write down three possible coordinates of a point $E$ such that triangle $BDE$ and triangle $ABD$ have the same area.</div></li></ol>

Two points $A$ and $B$ are marked in the Cartesian plane below.

Perimeter and Area of Parallelogram

Coordinates and Parallelogram Properties on a Cartesian Plane

Perimeter and Area of Plane Figures

<p>The grid below shows the triangle $PQR$.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760432515782-v5tz02fow8.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjA0MzI1MTU3ODItdjV0ejAyZm93OC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNzA5ODU2LCJleHAiOjE3OTI3MTAxNTZ9.tG6vb1GheqZzCl7wDjlUqzt5ura9-pclr2OeH-t2NAs" style="max-width: min(450px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-paragraph">State the gradient of the line $PQ$.</div></li><li><div class="list-item-paragraph">Find the gradient of the line $RQ$.</div></li><li><div class="list-item-paragraph">On the grid, draw and label the graph of $x=5$.</div></li><li><div class="list-item-paragraph">Write down the coordinates of $S$ such that&nbsp;$PQRS$ is a parallelogram.</div></li></ol>

Properties of Triangle  𝑃 𝑄 𝑅  on a Cartesian Grid

<p>The graph shows $3$ points ${A}$, ${B}$ and ${C}$.</p>
<figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760333112700-mzbta628klj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjAzMzMxMTI3MDAtbXpidGE2MjhrbGoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcwOTg1NiwiZXhwIjoxNzkyNzEwMTU2fQ.xBmWBmB4wmeL_Xo3q9CipdJv3NnQDFRuXgY4kE4r1KA" width="400" class="aligncenter" /></figure>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down the coordinates of point ${B}$.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">State the equation of the line ${BC}$.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Find the gradient of the line ${AB}$.</div><p style="text-align: right;">[1]</p></li></ol>

The graph shows $3$ points ${A}$, ${B}$ and ${C}$.

Equation of a Straight Line

2023 AISS EM S1 EOY P1 Q6

<p>${A}$ is the point ${(0, 5)}$ and the gradient of line ${AB}$ is ${-1.5}$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the equation of the line ${AB}$.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">The equation of line ${l}$ is ${2y + 3x = 6}$.</div><div class="list-item-paragraph">Explain why line ${l}$ does not intersect line ${AB}$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Line ${l}$ passes through the ${x}$-axis at point ${C}$ and ${y}$-axis at point ${D}$.</div><div class="list-item-paragraph">State the coordinates of</div><ol class="i-list"><li><div class="list-item-paragraph">point ${C}$,</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">point ${D}$,</div><p style="text-align: right;">[1]</p></li></ol></li></ol>

${A}$ is the point ${(0, 5)}$ and the gradient of line ${AB}$ is ${-1.5}$.

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