Coordinate Geometry (OCR GCSE Maths: Higher): Exam Questions

Here are the equations of four straight lines.

Line A   y = 2x + 4
Line B   2y = x + 4
Line C   2x + 2y = 4
Line D   2x – y = 4

Two of these lines are parallel.

Write down the two parallel lines?

$P$ 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.

$A$ 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.

$A,B$ 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 $C$.

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

$B$ ( ......... , .......... )

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

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 $Q$.

$\mathbf{A}$ 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.

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.

$$\begin{gathered} C(...........................,..........................) \\ D(...........................,..........................) \end{gathered}$$

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.

$ABC$ is a triangle in which angle $ABC=90°$

$p$ and $q$ are integers such that

the coordinates of $A$ are $(p,10)$
the coordinates of $B$ are (–1, –5 )
the coordinates of $C$are $(8,q)$

Given that the gradient of $AC$ is $-\frac{6}{7}$ work out the value of $p$ and the value of $q$

p = .......................................................
q = .......................................................

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 $T$.

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 $q$.

$Q,R$ 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 $A$.

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 $B$.