Coordinate Geometry (Cambridge (CIE) O Level Maths): Exam Questions

Find the mid-point of $AB$ where $A=(w,r)$ and  $B=(3w,t)$.

Give your answer in its simplest form in terms of $w$, $r$ and $t$.  

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

A is the point $(2,3)$ and B is the point $(7,-5)$.

Find the co-ordinates of the midpoint of AB.  

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

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

Work out the gradient of $AB$.

A straight line joins the points $(3k,6)$ and $(k,-5)$.
The line has a gradient of $2$.

Find the value of $k$.

$k$ = ................................................... 

P is the point (16, 9) and Q is the point (22, 24).

N is the point on PQ such that PN = 2NQ.

Find the co-ordinates of N.

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

$A$ 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.

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 $q$.

$\mathbf{A}$ and $\mathbf{B}$ are straight lines.
Line $\mathbf{A}$ has equation $2y=3x+8$
Line $\mathbf{B}$ goes through the points $(—1,2)$ and $(2,8)$

Do lines $\mathbf{A}$ and $\mathbf{B}$ intersect?
You must show all your working.