Coordinate Geometry (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

$A$ is the point $(2,7)$ and $B$ is the point $(–4,11)$.

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

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

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 $AB.$ 

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.

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

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

Calculate the length of AB.

The graphs of $y={\left(x-1\right)}^2$ 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.