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Grade 4 · Foundation and Higher · free GCSE maths worksheet

Midpoint of a line segment

Edexcel, AQA, OCR and Edexcel IGCSE

Averaging the x-coordinates and the y-coordinates of the two ends.

10 original questions, 23 marks. Type your answers below for an instant mark and a score, or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

How to do it

  1. Add the two x-coordinates together and halve: that is the x of the midpoint
  2. Add the two y-coordinates together and halve: that is the y of the midpoint
  3. Keep the minus signs when you add: -3 + 5 = 2, so halve it to get 1
  4. An odd total halves to a .5 answer, so (2 + 7) ÷ 2 = 4.5 is fine
  5. Given the midpoint and one end: double the midpoint, then subtract the end you know

Watch out: The midpoint is the average of the two points, so add the coordinates and halve - never subtract them.

Worked example

A is the point (−2, 7) and B is the point (5, 1).

Work out the coordinates of the midpoint of AB.

Add and halve each coordinate

x=-2 + 52 = 32 = 1.5
y=7 + 12 = 82 = 4

(1.5, 4)

The questions

1

A is the point (2, 4) and B is the point (8, 10).

Write down the coordinates of the midpoint of AB.

1 mark
Show answer
(5, 7)
2

P is the point (1, 6) and Q is the point (7, 2).

Write down the coordinates of the midpoint of PQ.

1 mark
Show answer
(4, 4)
3

C is the point (−4, 3) and D is the point (6, −5).

Work out the coordinates of the midpoint of CD.

2 marks
Show answer
(1, -1)
4

E is the point (2, 5) and F is the point (7, 8).

Work out the coordinates of the midpoint of EF.

2 marks
Show answer
(4.5, 6.5)
5

G is the point (−3, −7) and H is the point (−8, 2).

Work out the coordinates of the midpoint of GH.

2 marks
Show answer
(-5.5, -2.5)
6

M is the midpoint of the line segment PQ.

P is the point (4, −2) and M is the point (−1, 3.5).

Find the coordinates of Q.

3 marks
Show answer
(-6, 9)
7

ABCD is a rectangle drawn on a coordinate grid.

A is the point (1, 2) and C is the point (9, 8). A and C are opposite corners of the rectangle.

The diagonals of the rectangle cross at the centre of the rectangle.

Work out the coordinates of the centre of the rectangle.

2 marks
Show answer
(5, 5)
8

A circle is drawn on a coordinate grid.

The points (−3, 4) and (5, −2) are the two ends of a diameter of the circle.

Work out the coordinates of the centre of the circle.

2 marks
Show answer
(1, 1)
9

Amara and Ben are in a park. A map of the park uses a coordinate grid where 1 unit represents 1 km.

Amara is at the point (−5, 3) and Ben is at the point (2, −4). They walk in straight lines towards each other and meet at the point exactly halfway between them.

  1. Work out the coordinates of the point where they meet.
  2. Work out the distance Amara walks, in km. Give your answer correct to 2 decimal places.
4 marks
Show answer
a) (-1.5, -0.5) b) 4.95
10

M is the midpoint of the line segment AB.

A is the point (−4, 6) and M is the point (1, 2).

  1. Find the coordinates of B.
  2. Find the length of AB. Give your answer correct to 1 decimal place.
4 marks
Show answer
a) (6, -2) b) 12.8

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper. It is also on the Edexcel International GCSE (4MA1).

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