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<p>The diagram shows an isosceles triangle $PQR$, where&nbsp;$PQ=QR$ and the line segment $QR$ is parallel to the $y$-axis. Point $P$ lies on the $y$-axis and the equation of the line $PR$ is $x+3y=42$. Point $Q$ is $(-9,\ k)$, where&nbsp;$k$ is a positive constant.</p>
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<ol class="abc-list"><li data-list-item-id="cg-q11-a" data-list-item-path="cg-q11-a"><div class="list-item-paragraph">Find the coordinates of $P$, $Q$ and $R$.<span class="inline-marks">[4]</span></div></li><li data-list-item-id="cg-q11-b" data-list-item-path="cg-q11-b"><div class="list-item-paragraph">Given that the point $S$ is such that&nbsp;$PQRS$ is a kite and the line segment $RS$ is parallel to the $x$-axis, find the coordinates of $S$.<span class="inline-marks">[4]</span></div></li><li data-list-item-id="cg-q11-c" data-list-item-path="cg-q11-c"><div class="list-item-paragraph">Find the area of the kite $PQRS$.<span class="inline-marks">[2]</span></div></li></ol>

The diagram shows an isosceles triangle $PQR$, where $PQ=QR$ and the line segment $QR$ is parallel to the $y$-axis. Point $P$ lies on the $y$-axis and the equation of the line $PR$ is $x+3y=42$. Point $Q$ is $(-9,\ k)$, where $k$ is a positive constant.

Find the coordinates of $P$, $Q$ and $R$.

Given that the point $S$ is such that $PQRS$ is a kite and the line segment $RS$ is parallel to the $x$-axis, find the coordinates of $S$.

Length of a Line Segment

Area of Rectilinear Figures

Equation of a Straight Line

Isosceles triangle extended to a kite

Coordinate Geometry

<p>The diagram shows a rectangle $ABCD$ in which $A$ and $C$ lie on the $x$-axis. The equation of $AB$ is $3y=x+1$ and the equation of $BD$ is $4y=3x-12$.</p>
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<p>Find</p>
<ol class="i-list"><li data-list-item-id="cg-q04-i" data-list-item-path="cg-q04-i"><div class="list-item-paragraph">the coordinates of $B$,<span class="inline-marks">[2]</span></div></li><li data-list-item-id="cg-q04-ii" data-list-item-path="cg-q04-ii"><div class="list-item-paragraph">the coordinates of the midpoint of $AC$,<span class="inline-marks">[2]</span></div></li><li data-list-item-id="cg-q04-iii" data-list-item-path="cg-q04-iii"><div class="list-item-paragraph">the coordinates of $A$, $C$ and $D$,<span class="inline-marks">[4]</span></div></li><li data-list-item-id="cg-q04-iv" data-list-item-path="cg-q04-iv"><div class="list-item-paragraph">the length of $BC$,<span class="inline-marks">[2]</span></div></li><li data-list-item-id="cg-q04-v" data-list-item-path="cg-q04-v"><div class="list-item-paragraph">the area of the rectangle $ABCD$.<span class="inline-marks">[2]</span></div></li></ol>

The diagram shows a rectangle $ABCD$ in which $A$ and $C$ lie on the $x$-axis. The equation of $AB$ is $3y=x+1$ and the equation of $BD$ is $4y=3x-12$.

the coordinates of the midpoint of $AC$,

the coordinates of $A$, $C$ and $D$,

Intersection of Two Lines

Midpoint of a Line Segment

Rectangle with a diagonal along the x-axis

<p>The diagram shows a rectangle $ABCD$ in which $A$ is $(1,\ 2)$ and $D$ is $(5,\ 0)$. The diagonal $AC$ lies on the line $y=x+1$.</p>
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<p>Find</p>
<ol class="i-list"><li data-list-item-id="cg-q03-i" data-list-item-path="cg-q03-i"><div class="list-item-paragraph">the equation of $CD$,<span class="inline-marks">[3]</span></div></li><li data-list-item-id="cg-q03-ii" data-list-item-path="cg-q03-ii"><div class="list-item-paragraph">the coordinates of $C$ and of $B$,<span class="inline-marks">[4]</span></div></li><li data-list-item-id="cg-q03-iii" data-list-item-path="cg-q03-iii"><div class="list-item-paragraph">the length of $AB$,<span class="inline-marks">[2]</span></div></li><li data-list-item-id="cg-q03-iv" data-list-item-path="cg-q03-iv"><div class="list-item-paragraph">the area of the rectangle $ABCD$.<span class="inline-marks">[2]</span></div></li></ol>

The diagram shows a rectangle $ABCD$ in which $A$ is $(1,\ 2)$ and $D$ is $(5,\ 0)$. The diagonal $AC$ lies on the line $y=x+1$.

Parallel and Perpendicular Lines

Rectangle from a vertex pair and a diagonal

<p>The diagram shows the points $A(-7,\ 5)$ and $B(5,\ -4)$.</p>
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<p>Find</p>
<ol class="i-list"><li data-list-item-id="cg-q01-i" data-list-item-path="cg-q01-i"><div class="list-item-paragraph">the length of $AB$,<span class="inline-marks">[2]</span></div></li><li data-list-item-id="cg-q01-ii" data-list-item-path="cg-q01-ii"><div class="list-item-paragraph">the coordinates of the midpoint of $AB$,<span class="inline-marks">[1]</span></div></li><li data-list-item-id="cg-q01-iii" data-list-item-path="cg-q01-iii"><div class="list-item-paragraph">the gradient of $AB$,<span class="inline-marks">[1]</span></div></li><li data-list-item-id="cg-q01-iv" data-list-item-path="cg-q01-iv"><div class="list-item-paragraph">the equation of $AB$.<span class="inline-marks">[2]</span></div></li></ol>

The diagram shows the points $A(-7,\ 5)$ and $B(5,\ -4)$.

the coordinates of the midpoint of $AB$,

Gradient of a Straight Line

Length, midpoint, gradient and equation from two points

<p>The line $y = x - 4$ and the curve $y = \frac{2}{x - 3}$ intersect at the points $A$ and $B$.</p>
<p>Find the length of $AB$.<span class="inline-marks">[6]</span></p>

The line $y=x-4$ and the curve $y=\frac{2}{x-3}$ intersect at the points $A$ and $B$.

Intersection of a Line and a Curve

2025 DSS PRELIMS P1 Q1

Quadratic Functions, Equations and Inequalities

<p>The straight line $2x + y = 1$ intersects the curve $x^2 - xy - y^2 + 5 = 0$ at the points $A$ and $B$.</p>
<p>Show that the length $AB$ is $5\sqrt{5}$ units.<span class="inline-marks">[5]</span></p>

The straight line $2x + y = 1$ intersects the curve $x^2 - xy - y^2 + 5 = 0$ at the points $A$ and $B$.

Show that the length $AB$ is $5\sqrt{5}$ units.

2025 SCGS PRELIMS P1 Q2

<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/1770805603072-58nwvw5dd8k.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzA4MDU2MDMwNzItNThud3Z3NWRkOGsucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTkwNCwiZXhwIjoxNzkyNjk2MjA0fQ.LCKCy2brRlvg-oaa64xG9gQSpuSpVmbbhtCma-Bl3AM" style="max-width: min(250px, 100%); height: auto; display: block;" alt="The diagram shows an isosceles triangle $PQR$ on a coordinate plane." class="aligncenter custom-width" /></figure></div>
<p>The diagram shows an isosceles triangle $PQR$ with vertices at $P(0, k)$, $Q(3, 9)$ and $R(h, 6)$, where&nbsp;$h$ and $k$ are positive constants and $h &gt; k$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Show that&nbsp;$h + k = 12$.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">It is now given that&nbsp;$h = 7$.<br>The point $S$ is such that&nbsp;$PQRS$ is a kite. Given that&nbsp;$S$ lies on the line $21y = 7x - 8$, find the coordinates of $S$.<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">Find the area of the kite.<span class="inline-marks">[2]</span></div></li></ol>

The diagram shows an isosceles triangle $PQR$ with vertices at $P(0, k)$, $Q(3, 9)$ and $R(h, 6)$, where $h$ and $k$ are positive constants and $h > k$.

It is now given that $h = 7$.\nThe point $S$ is such that $PQRS$ is a kite. Given that $S$ lies on the line $21y = 7x - 8$, find the coordinates of $S$.

Perpendicular Bisectors

IP3 Class Test (May 2025) Q11 (2023 ACSBR AM Prelim P2 Q5)

<p>The line passing through the points $P(-2, 5)$ and $Q(q, 8)$ is parallel to the line $3x + 4y + 4 = 0$.</p>
<p>Find the</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">value of $q$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">distance $PQ$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">equation of the perpendicular bisector of $PQ$.</span></div></li></ol>

The line passing through the points $P(-2, 5)$ and $Q(q, 8)$ is parallel to the line $3x + 4y + 4 = 0$.

equation of the perpendicular bisector of $PQ$.

<p>Three points have coordinates $P(-3, 4)$, $Q(7, -2)$ and $R(5, m)$. Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the value of $m$ if&nbsp;$PQ$ is perpendicular to $PR$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the midpoint of $PQ$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the equation of the perpendicular bisector of $PQ$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the lengths of $PQ$ and $PR$,</span></div></li><li><div class="list-item-paragraph">the area of triangle $PQR$, using the results in <strong>(d)</strong>.</div></li></ol>

Three points have coordinates $P(-3, 4)$, $Q(7, -2)$ and $R(5, m)$. Find

the value of $m$ if $PQ$ is perpendicular to $PR$,

the equation of the perpendicular bisector of $PQ$,

<p>Three points have coordinates $A(1, 8)$, $B(0, 3)$ and $C(k, 5)$. Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the value of $k$ if&nbsp;$AC$ is perpendicular to $BC$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the midpoint of $AB$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the equation of the perpendicular bisector of $AB$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the lengths of $AB$ and $BC$,</span></div></li><li><div class="list-item-paragraph">the area of triangle $ABC$, using the results in <strong>(d)</strong>.</div></li></ol>

Three points have coordinates $A(1, 8)$, $B(0, 3)$ and $C(k, 5)$. Find

the value of $k$ if $AC$ is perpendicular to $BC$,

the equation of the perpendicular bisector of $AB$,

<p>A circle $C$ is given by the equation $3x^2 + 3y^2 + 9x - 15y - 39 = 0$.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-content"><span class="list-item-text">Find the coordinates of the centre of the circle and the radius of the circle.</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-content"><span class="list-item-text">Determine, with working, if the point $(-3, 5)$ lies inside or outside the circle.</span></div></li></ol>
<p>Another circle $M$, with centre $\left( \frac{\sqrt{123} - 3}{2}, 12 \right)$, touches the circle $C$ at one point. Find</p>
<ol class="abc-list" start="3"><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-content"><span class="list-item-text">the distance between the two centres.</span></div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-content"><span class="list-item-text">all possible equations of $M$ in the form $x^2 + y^2 + 2gx + 2fy + c = 0$.</span></div></li></ol>

A circle $C$ is given by the equation $3x^2 + 3y^2 + 9x - 15y - 39 = 0$.

Find the coordinates of the centre of the circle and the radius of the circle.

Determine, with working, if the point $(-3, 5)$ lies inside or outside the circle.

Another circle $M$, with centre $\left( \frac{\sqrt{123} - 3}{2}, 12 \right)$, touches the circle $C$ at one point. Find

all possible equations of $M$ in the form $x^2 + y^2 + 2gx + 2fy + c = 0$.

Finding the Centre and Radius of a Circle

Problems Involving Two Circles

Position of a Point Relative to a Circle

<p>A circle $C$ passes through the point $P \ (-6, 6)$ and has the same centre as the circle $x^{2} + y^{2} + 6x - 4y + 2 = 0$.</p>
<ol class="abc-list"><li data-list-item-id="item-a"><div class="list-item-content"><span class="list-item-text">Find the equation of the circle $C$.</span></div></li><li data-list-item-id="item-b"><div class="list-item-paragraph">Find the equation of the tangent to the circle $C$, at the point $ (-6,6) $.</div></li></ol>
<p>Another point $Q \ (-6, q)$ which lies on circle $C$, is the same distance from the $y$-axis as the point $P$.</p>
<ol class="abc-list" start="4"><li data-list-item-id="item-c"><div class="list-item-content"><span class="list-item-text">Find the coordinates of the point $Q$.</span></div></li><li data-list-item-id="item-d"><div class="list-item-content"><span class="list-item-text">Find the perimeter of the triangle $POQ$, where&nbsp;$O$ is the centre of the circle $C$.</span></div></li></ol>

A circle $C$ passes through the point $P \ (-6, 6)$ and has the same centre as the circle $x^{2} + y^{2} + 6x - 4y + 2 = 0$.

Another point $Q \ (-6, q)$ which lies on circle $C$, is the same distance from the $y$-axis as the point $P$.

Find the perimeter of the triangle $POQ$, where $O$ is the centre of the circle $C$.

Finding the Equation of a Circle

Tangents and Normals to Circles

Line–Circle Intersections

<p><strong>Solutions to this question by accurate drawing will not be accepted.</strong></p>
<p>Given three of the vertices of a parallelogram $ABCD$ are $A(-3,-7)$, $B(1,4)$, $C(10,3)$. Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the distance between points $A$ and $B$, correct to $3$ significant figures,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the midpoint of the diagonal $AC$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the coordinates of the fourth vertex $D$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the equation of the line $CD$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the area of the parallelogram $ABCD$.</span></div></li></ol>

**Solutions to this question by accurate drawing will not be accepted.**

Given three of the vertices of a parallelogram $ABCD$ are $A(-3,-7)$, $B(1,4)$, $C(10,3)$. Find

the distance between points $A$ and $B$, correct to $3$ significant figures,

the coordinates of the fourth vertex $D$,

<p>The line passing through the points $A(-5, 7)$ and $T(t, 8)$ is parallel to the line $6x + 4y - 7 = 0$.</p>
<p>Find the</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">value of $t$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">distance $AT$.</span></div></li></ol>

The line passing through the points $A(-5, 7)$ and $T(t, 8)$ is parallel to the line $6x + 4y - 7 = 0$.

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>A line joining the points $A(-3,1)$ and $B(2,-3)$<br>Work out the length of line $AB$.<br>Give your answer to $3$ decimal places.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><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/1768906942860-mdjbaji00de.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njg5MDY5NDI4NjAtbWRqYmFqaTAwZGUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTkwNCwiZXhwIjoxNzkyNjk2MjA0fQ.YRP6-kk4eq328I2A_7eiH-kIFYBCC_N8S0gsSsf4XNs" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

IP1U13 SWII (Pythagoras) Q3

<p>In the diagram $R$ is the point $\left( 0,-4 \right)$ and $P$ is a point on the $y$-axis.<br>The line $PQ$ meets the horizontal line through $R$ at $Q$.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">State the equation of $QR$.</div></li><li><div class="list-item-paragraph">Given that the equation of the line $PQ$ is $2y-5x-4=0$, find the coordinates of $P$ and $Q$.</div></li><li><div class="list-item-paragraph">Given that the length of $PQ$ is $\sqrt{t}$, find the value of $t$.</div></li><li><div class="list-item-paragraph">Find the area of triangle $PQR$.</div></li><li><div class="list-item-paragraph">Hence, calculate the perpendicular distance from $R$ to $PQ$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765900124482-mmithszwr5d.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU5MDAxMjQ0ODItbW1pdGhzendyNWQucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTkwNCwiZXhwIjoxNzkyNjk2MjA0fQ.U5lLCgDXXpT1UJ6E0OBQqOgTF3xvEL-aUf7E-psY8-I" style="max-width: min(400px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

In the diagram $R$ is the point $\left( 0,-4 \right)$ and $P$ is a point on the $y$-axis.
The line $PQ$ meets the horizontal line through $R$ at $Q$.

Distance from a Point to a Line

Coordinate Geometry with Line Intersections and Perpendicular Distance

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>The diagram shows the points $P\left( 0,2 \right)$ and $Q\left( 0,12 \right)$.<br>$QR$ and $PR$ are straight lines.</p><ol class="i-list"><li><div class="list-item-paragraph">Given that the equation of the line $QR$ is parallel to the line $y=-2x+5$, write down the equation of the line $QR$.</div></li><li><div class="list-item-paragraph">If&nbsp;$PR$ is a horizontal line <strong>parallel</strong> to the $x$-axis, state the equation of $PR$.</div></li><li><div class="list-item-paragraph">Given that the $x$-coordinate of $R$ is $r$. Calculate</div><ol class="abc-list"><li><div class="list-item-paragraph">the value of $r$.</div></li><li><div class="list-item-paragraph">the length of $QR$.</div></li></ol></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><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/1765896119067-nzvpeb75s0r.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU4OTYxMTkwNjctbnp2cGViNzVzMHIucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTkwNCwiZXhwIjoxNzkyNjk2MjA0fQ.yMjm6ic_Br0sWu9Cp_BBBqfvQlcy7dMY6z5KoaqceSk" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

Solving problem involving coordinates

<p>The coordinates of $Q$ and $R$ are $\left( 7,6 \right)$ and $\left( 2,-1 \right)$ respectively.</p>
<p>Given that&nbsp;$P$ is a point on $x$-axis such that&nbsp;$PR=\frac{1}{2}PQ$, find the two possible coordinates of $P$.</p>

The coordinates of $Q$ and $R$ are $\left( 7,6 \right)$ and $\left( 2,-1 \right)$ respectively.

Given that $P$ is a point on $x$-axis such that $PR=\frac{1}{2}PQ$, find the two possible coordinates of $P$.

<p>The diagram shows the graph of $y=8-x$. <br>The graph intersects the $x$-axis and $y$-axis at points $A$ and $B$ respectively.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">Write down the coordinates of $A$ and $B$.</div></li><li><div class="list-item-paragraph">Calculate the length of the line segment $AB$.  </div></li><li><div class="list-item-paragraph">Calculate the area of triangle $AOB$.  <br>Hence, calculate the shortest distance from point $O$ to the line $AB$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765871800920-x8q8ggsxsvk.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU4NzE4MDA5MjAteDhxOGdnc3hzdmsucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTkwNCwiZXhwIjoxNzkyNjk2MjA0fQ.KGVPJS0bX7Zj1-ZFBfAXoSs60wNPJgveGxFzT5I8cKk" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The diagram shows the graph of $y=8-x$. 
The graph intersects the $x$-axis and $y$-axis at points $A$ and $B$ respectively.

Coordinate Geometry: Line Intercepts and Triangle Area

<p>Triangle $PQR$ has vertices $P\left( 1,1 \right)$, $Q\left( 3,2 \right)$ and $R\left( 2,4 \right)$.</p>
<ol class="i-list"><li data-list-item-id="item-1765871630044-sthrjxqzp" data-list-item-path="item-1765871630044-sthrjxqzp"><div class="list-item-paragraph">Calculate the length of $PQ$, $QR$ and $PR$, giving your answers correct to $3$ significant figures.</div></li><li data-list-item-id="item-1765871630676-0yr44p99s" data-list-item-path="item-1765871630676-0yr44p99s"><div class="list-item-paragraph">What can you conclude about triangle $PQR$? Explain.</div></li></ol>

Triangle $PQR$ has vertices $P\left( 1,1 \right)$, $Q\left( 3,2 \right)$ and $R\left( 2,4 \right)$.

Math Question Bank