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Midpoint of a line segment – GCSE Maths

Foundation and Higher · Grade 5 · Non-calculator

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Find the point halfway along a line segment by averaging the -coordinates and averaging the -coordinates. It is on Foundation and Higher, aimed at grade 5. Free questions with answers are on this page. Worked examples show each line before you try the questions.

The midpoint of and is — average the s, average the s. If M is the midpoint of A and B and you know A and M, B is as far again the other side: .

A 'centre of a line segment' question on a geometry diagram is this formula, not a guess from counting squares (though counting squares is a fine check). Keep fractions: midpoint of and is , not a rounded .

Average the s and average the s. To find an endpoint from a midpoint, take the same jump again: from to is the vector, then plus that vector is .

Objectives

Key points

Worked examples

Example 1

Work out the coordinates of the midpoint of (2, 6) and (8, 2).

2 marks

  1. Add the x-coordinates and halve: (2 + 8) / 2 = 5
  2. Add the y-coordinates and halve: (6 + 2) / 2 = 4
  3. Write as a coordinate pair: (5, 4)

Answer: (5, 4)

Common slips
  • Slip: Archie did 2 + 8 = 10 without halving The midpoint requires finding the average of each coordinate.
  • Slip: Amber subtracted the x-coordinates: 8 - 2 = 6. Subtracting finds the gap between the points, not the middle. Add, then halve.
  • Slip: Archie wrote (10, 8) A midpoint must be halved.

Example 2

Work out the x-coordinate of the midpoint of (1, 8) and (7, 2).

2 marks

  1. Identify the x-coordinates of the endpoints: 1 and 7
  2. Calculate the average: (1 + 7) / 2 = 8 / 2 = 4
  3. State the requested single coordinate: 4

Answer: 4

Common slips
  • Slip: Boris took the y-coordinates 8 and 2 The question asks specifically for the x-coordinate.
  • Slip: Bella did (8 + 2) / 2 = 5 Average only the x-coordinates.
  • Slip: Bella wrote (4, 5) Give only the x-coordinate as requested.

Example 3

Work out the distance between (1, 2) and (4, 6).

3 marks

  1. Find horizontal change: dx = 4 - 1 = 3
  2. Find vertical change: dy = 6 - 2 = 4
  3. Apply Pythagoras: √(3^2 + 4^2) = √(9 + 16) = √25 = 5

Answer: 5

Common slips
  • Slip: Cameron added 1 + 4 = 5 Calculate difference between x-coordinates.
  • Slip: Cameron added 2 + 6 = 8 Calculate difference between y-coordinates.
  • Slip: Cameron added dx + dy = 7 Distance uses the Pythagorean theorem.

Questions and answers

GCSE Maths midpoint of a line segment questions and answers. Try each one, then open the answer. Easy questions come first.

Question 1 Easy2 marks

Work out the coordinates of the midpoint of (0, 0) and (4, 6).

Show answer

Answer: (2, 3)

  1. x-midpoint: (0 + 4)/2 = 2.
  2. y-midpoint: (0 + 6)/2 = 3.
  • M1 — x-midpoint: (0 + 4)/2 = 2.
  • A1 — y-midpoint: (0 + 6)/2 = 3.

Question 2 Easy2 marks

Work out the coordinates of the midpoint of (1, 2) and (5, 8).

Show answer

Answer: (3, 5)

  1. x-midpoint: (1 + 5)/2 = 3.
  2. y-midpoint: (2 + 8)/2 = 5.
  • M1 — x-midpoint: (1 + 5)/2 = 3.
  • A1 — y-midpoint: (2 + 8)/2 = 5.

Question 3 Medium2 marks

Work out the x-coordinate of the midpoint of (0, 3) and (6, 1).

Show answer

Answer: 3

  1. Identify x-values 0 and 6.
  2. Average: (0 + 6)/2 = 3.
  • M1 — Identify x-values 0 and 6.
  • A1 — Average: (0 + 6)/2 = 3.

Question 4 Medium2 marks

Work out the x-coordinate of the midpoint of (2, 9) and (8, 1).

Show answer

Answer: 5

  1. Identify x-values 2 and 8.
  2. Average: (2 + 8)/2 = 5.
  • M1 — Identify x-values 2 and 8.
  • A1 — Average: (2 + 8)/2 = 5.

Question 5 Hard2 marks

Work out the distance between (0, 0) and (6, 8).

Show answer

Answer: 10

  1. dx = 6, dy = 8.
  2. Distance = √(36 + 64) = √100 = 10.
  • M1 — dx = 6, dy = 8.
  • A1 — Distance = √(36 + 64) = √100 = 10.

Question 6 Hard2 marks

Work out the distance between (0, 0) and (5, 12).

Show answer

Answer: 13

  1. dx = 5, dy = 12.
  2. Distance = √(25 + 144) = √169 = 13.
  • M1 — dx = 5, dy = 12.
  • A1 — Distance = √(25 + 144) = √169 = 13.

Question 7 Exam-style3 marks

Work out the distance between (1, 2) and (7, 10).

Show answer

Answer: 10

  1. Calculate horizontal and vertical changes: dx = 6, dy = 8.
  2. Apply Pythagoras: √(36 + 64) = √100 = 10.
  • M1 — Differences 6 and 8 found
  • M1 — 6^2 + 8^2 = 100
  • A1 — 10

Common mistakes

Most lost marks on this topic are one slip.

  1. Adding coordinates without halving

    Midpoint is the average: divide by 2

  2. Mixing x and y coordinates

    Average x with x and y with y separately

  3. Adding differences instead of using Pythagoras for distance

    Distance between points requires √(dx^2 + dy^2)

Spot the slip

Work out the midpoint of (2, 6) and (8, 2). Ada adds the coordinates in each pair and does not halve. What is the correct midpoint?

  1. (5, 4)
  2. (10, 8)
  3. (6, 4)
Show the slip

(5, 4) The averages are (2+8)/2 and (6+2)/2.

Exam tips

Printable worksheet

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Questions students ask

Is Midpoint of a line segment Foundation or Higher?

Midpoint of a line segment is on Foundation and Higher, aimed at grade 5.

What is a common slip on Midpoint of a line segment?

Adding coordinates without halving. Midpoint is the average: divide by 2.

Where can I get Midpoint of a line segment questions and answers?

The questions on this page are free. Open Show answer under each one, or download the worksheet PDF. Start free to practise this topic in the app.

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Last updated 9 November 2026.

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