GCSE · Straight-line graphs

Coordinates and midpoints (four quadrants, missing corners, ratio on a line)Exam-style questions

How two numbers in brackets pin down a point in all four quadrants (across first, then up or down), lines where one coordinate never changes, how to find the missing corner of a shape, the midpoint of a line segment and the other end from a midpoint, and how to find the point that splits a line segment in a given ratio.

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12 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4

1
A map is drawn on a coordinate grid.

A cycle path on the map is a straight line.

It starts at $P(-5, -1)$ , passes through $Q(1, 5)$ and ends at $R$ .

$QR = \frac{2}{3}PQ$

Find the coordinates of $R$ .

You must show all your working.

(3 marks)
Level 4 · 3 marksTry it
2
On a plan of a garden, a straight path runs from the shed at $S(-6, 8)$ to the pond at $P(9, -2)$ .

A bird table $B$ stands on the path so that

$SB : BP = 2 : 3$

Work out the coordinates of $B$ .

(3 marks)
Level 4 · 3 marksTry it
3
$Q$ is the point $(-3, -5)$ and $R$ is the point $(9, 1)$ .

$P$ is the point on the line segment $QR$ such that $QP = \frac{3}{4}QR$ .

Find the coordinates of $P$ .

You must show your working.

(3 marks)
Level 4 · 3 marksTry it
4
$ABCD$ is a parallelogram.

$A$ is the point $(-2, 3)$ , $B$ is the point $(6, 5)$ and $C$ is the point $(8, -1)$ .

The diagonals $AC$ and $BD$ cross at the point $M$ .
(a) Work out the coordinates of $M$ .

(2 marks)
(b) Work out the coordinates of $D$ .

(2 marks)
Level 4 · 4 marksTry it
5
$A$ is the point $(-4, -7)$ and $B$ is the point $(6, 8)$ .

The point $P$ divides the line segment $AB$ in the ratio $2 : 3$ .
(a) Find the coordinates of $P$ .

(3 marks)

Sam says,

" $P$ lies on the line with equation $y = 3x - 1$ ."
(b) Is Sam correct?

You must give a reason for your answer.

(1 mark)
Level 4 · 4 marksTry it