Coordinate Geometry (Edexcel IGCSE Maths): Exam Questions

Triangle $HJK$ is isosceles with $HJ=HK$ and $JK=\sqrt{80}$

$H$ is the point with coordinates $(-4,1)$ $J$ is the point with coordinates $(j,15)$ where $j<0$ $K$ is the point with coordinates $(6,k)$

$M$is the midpoint of $JK$. The gradient of $HM$ is 2

Find the value of $j$and the value of $k$.

$A$ and $B$are two points.

Point $A$ has coordinates (—2, 4). Point $B$ has coordinates (8, 9).

$C$ is the midpoint of the line segment $AB$.

Find the coordinates of $C$.

$D$ is the point with coordinates (100, 56).

Does point $D$ lie on the straight line that passes through $A$ and $B$? You must show how you work out your answer.

$A$ is the point (—1, 2) $B$ is the point (7, 5)

Find the coordinates of the midpoint of $AB$.

$P$ is the point (—4, 4) $Q$ is the point (1, —5)

Find the gradient of $PQ$.

The point $A$ has coordinates (2, 3). The point $B$ has coordinates (6, 8).

$M$ is the midpoint of the line $AB$. Find the coordinates of $M$.

$Q,R$ and $S$ are points on a grid.

$Q$ is the point with coordinates (106, 103) $R$ is the point with coordinates (106, 105) $S$ is the point with coordinates (104, 105.5)

$P$ and $A$ are two other points on the grid such that

$R$ is the midpoint of $PQ$
$S$ is the midpoint of $PA$

Work out the coordinates of the point $A$.

Point $P$ has coordinates (5, 7). Point $M$ has coordinates (1, 2.5).

Point $M$ is the midpoint of the line $PQ$.

Find the coordinates of point $Q$.

The straight line $L$ has equation $2y+7x=10$

Find the gradient of $L$

A triangle has vertices $P,Q$ and $R$.

The coordinates of $P$ are (—3, —6) The coordinates of $Q$ are (1, 4) The coordinates of $R$ are (5, —2)

$M$ is the midpoint of $PQ$. $N$ is the midpoint of $QR$.

Prove that $MN$ is parallel to $PR$. You must show each stage of your working.

Point $A$ has coordinates $(--3,11)$ Point $B$ has coordinates $(47,b)$ The midpoint of $AB$ has coordinates $(a,--19)$

Find the value of $a$ and the value of $b$.

a = ................................................

b = ................................................

Point $A$ has coordinates (5, 8) Point $B$ has coordinates (9, –4)

Work out the gradient of $AB$.

A pattern is made from four identical squares.

The sides of the squares are parallel to the axes.

Point $A$ has coordinates (6, 7) Point $B$ has coordinates (38, 36) Point $C$ is marked on the diagram.

Work out the coordinates of $C$.

AB is a line segment.

A is the point with coordinates (3, 6, 7). The midpoint of AB has coordinates (−2, 2, 5).

Find the coordinates of* B.*

The point* *$A$ has coordinates (5, −4) The point $B$ has coordinates (13, 1)

Work out the coordinates of the midpoint of $AB$.

Line $L$ has equation $y=2-3x$

Write down the gradient of line $L$.

$A$ and $B$ are straight lines.

Line $A$ has equation $2y=3x+8$ Line $B$ goes through the points $(---1,2)$ and $(2,8)$

Do lines $A$ and $B$ intersect? You must show all your working.

Here is a cuboid drawn on a 3-D grid.

$P$ is a vertex of the cuboid.

$T$ divides the line $OP$ in the ratio 1 : 2

Find the coordinates of $T$.

Find the gradient of the straight line with equation $5x+2y=7$

A rectangle $ABCD$ is to be drawn on a centimetre grid such that

$A$ has coordinates (–4, –2) $B$ has coordinates (1, 10) $C$ has coordinates (19, $a$) $D$ has coordinates $(b,c)$

Work out the value of $a$, the value of $b$ and the value of $c$.

$a=.................................\,b=.................................\,c=.................................$

Calculate the perimeter, in centimetres, of rectangle ABCD.

...................................................... cm

The points $A,B$ and $C$ lie in order on a straight line.

The coordinates of $A$ are (2, 5) The coordinates of $B$ are (4, $p$) The coordinates of $C$ are ($q$, 17)

Given that $AC=4AB$, find the values of $p$ and $q$.

$A$ is (2, 13) and $B$ is (10, 1)

Circle the midpoint of $AB$.

The diagram shows a line joining $O$ to $P$.

The gradient of the line is 2

The length of the line is $\sqrt{2645}$

Work out the coordinates of $P.$

$P$ is the point (2, 14) $Q$ is the point (6, 8) $R$is the point (2, 5)

Use gradients to show that angle $PQR$ is not a right angle.

$P$ is (4, 9) and $Q$ is (–2, 1) Circle the midpoint of $PQ$.

A pattern is made from four congruent right-angled triangles.

The line AC is parallel to the *x *- axis. The point A has coordinates (4, 9) and the point B has coordinates (17, 12).

Work out the coordinates of point C and point D.

$C(...........................,..........................)\,D(...........................,..........................)$

$A$ (0, 2) and $B$ (6, 5) are points on the straight line $ABCD$.

$AB=BC=CD$ Work out the coordinates of $D$.

Circle the point that does not lie on the curve $y=x^{3}$

A straight line goes through the points ($p,q$) and ($r,s$), where

• $p+2=r$
• $q+4=s.$

Find the gradient of the line.

$A$ is the point (2, –5)

$B$ is the point (4, –9)

Show that the gradient of the straight line passing through $A$ and $B$ is –2

$C$ is the point (–301, 601)

Does $C$lie on the straight line passing through $A$and $B$?

You must show your working.

$A$ is (2, 12) and $B$ is (8, 2) Circle the midpoint of $AB$.

$A,B$ and $C$ are points on the axes as shown.

The area of triangle $ABC$ is 28 square units.

Work out possible coordinates for $A,B$ and $C$.

$A$ ( ......... , .......... )

$B$ ( ......... , .......... )

$C$ ( ......... , .......... )

Work out the gradient of the straight line through (–2, 3) and (1, 9)

A straight line is drawn on the centimetre grid.

Fay assumes that the scale is 1 cm represents 1 unit.

Use her assumption to work out the gradient of the line.

In fact, the scale is 1 cm represents 2 units.

Which statement is correct? Tick one box.

square The answer to part (a) is too big

square The answer to part (a) stays the same

square The answer to part (a) is too small