Coordinate Geometry (Cambridge International IGCSE Mathematics): Exam Questions

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 $M$.

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

Find the gradient of $L$.

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

Work out the gradient of $AB$.

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 $L$.

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

Point $A$ has coordinates $( - 3 , 5 )$.

Point $B$ has coordinates $( 9 , 10 )$.

Work out the midpoint of the two points.

Find the length between the points $A$ and $B$.

A is the point (7, 2) and B is the point (−5, 8).

Calculate the length of AB.

A rhombus $ABCD$ has a diagonal $AC$ where $A$ is the point $(-3,10)$ and C is the point $(4,-4).$

Calculate the length $AC.$

The coordinates of P are $(-3,8)$ and the coordinates of Q are $(9,-2)$.

Calculate the length PQ.

A is the point (2, 1) and B is the point (9, 4).

Find the length of AB.

$A$ is the point $(8,5)$ and $B$ is the point $(-4,1)$.

Calculate the length of $AB.$

Extract:

A is the point (8, 5) and B is the point (−4, 1).

Find the co-ordinates of the midpoint of $AB.$

( ..................... , ..................... )

$A$ is the point $(7,12)$and $B$ is the point $(2,-1)$.

Find the length of $AB$.

C is the point (8, 14).

Calculate the length of AC.

Extract:

C is the point (8, 14).

Find the co-ordinates of the mid-point of BC.

( ..................... , ......................)

Calculate the length of AB.

The graphs of $y = ( x - 1 )^{2}$ and $y=\frac{1}{2}x+1$ intersect at A and B.

Find the length of AB.

AB = ................................................

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.

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 $P.$

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.

$P$ is the point $( 3 , 14 )$ and $Q$ is the point $( - 1 , 2 )$.

Calculate the length of $PQ$.

Extract:

$P$ is the point $\left(3 , 14\right)$ and $Q$ is the point $\left(- 1 , 2\right)$.

Find the equation of the line that is perpendicular to $PQ$ and that passes through the point $( - 6 , 7 )$.

Give your answer in the form $y=mx+c$.