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.

Start practising Read the lesson

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

DifficultyAll Level 3 Level 4

1
$M$ is the midpoint of the line segment $PQ$ .

$P$ has coordinates $(-2, 5)$ .

$M$ has coordinates $(3, 1)$ .

Find the coordinates of $Q$ .

(2 marks)
Level 3 · 2 marksTry it
2
$A$ is the point $(-5, 4)$ and $B$ is the point $(2, -3)$ .

Work out the coordinates of the midpoint of $AB$ .

(2 marks)
Level 3 · 2 marksTry it
3
The diagram shows three vertices of parallelogram $ABCD$ .Not to scale

$A$ is at $(1, 2)$ , $B$ is at $(3, 7)$ and $C$ is at $(10, 7)$ .

Find the coordinates of $D$ .

(2 marks)
Level 3 · 2 marksTry it
4
Points $A(-3, -1)$ , $B(1, -1)$ and $C(1, 2)$ are three vertices of a parallelogram.(a) Work out the coordinates of one possible position of the fourth vertex.

(1 mark)
(b) Kai says,

"There is only one possible position for the fourth vertex."

Is Kai correct?

Tick a box.

Yes $\square$ $\qquad\qquad$ No $\square$

Give a reason for your answer.

(1 mark)
Level 3 · 2 marksTry it
5
Lena is asked to find the midpoint of the line segment joining $(-7, 2)$ and $(3, -6)$ .

Here is her working.

$3 - (-7) = 10, \qquad 10 \div 2 = 5$

$-6 - 2 = -8, \qquad -8 \div 2 = -4$

Midpoint $= (5, -4)$
(a) What mistake has Lena made?

(1 mark)
(b) Work out the correct coordinates of the midpoint.

(2 marks)
Level 3 · 3 marksTry it

2 more questions on coordinates and midpoints (four quadrants, missing corners, ratio on a line)

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free