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Midpoint and length of a line segment questions and answers

The midpoint of the line from (x1,y1)(x_1, y_1) to (x2,y2)(x_2, y_2) is (x1+x22,y1+y22)\left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right): the average of the x-coordinates and the average of the y-coordinates. The length of the line uses Pythagoras: (x2−x1)2+(y2−y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

8 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated .

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Where midpoint and length of a line segment comes up

GCSE (AQA, Edexcel, OCR)Foundation and Higher: work with coordinates in all four quadrants. Lengths use Pythagoras' theorem.
Cambridge IGCSE (0580)Extended only: calculate the length and find the midpoint of a line segment, and the perpendicular bisector of a line.
Edexcel International GCSE (4MA1)Foundation and Higher: determine the coordinates of the midpoint of a line segment, given the coordinates of the two end points.

The method

  1. Midpoint: add the x-coordinates and halve; add the y-coordinates and halve.
  2. Missing end point: the step from A to M is the same as from M to B.
  3. Length: difference in x, difference in y, then Pythagoras.

Midpoint and length of a line segment questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Find the midpoint of (2,4)(2, 4) and (8,10)(8, 10).

Question 2Warm-upFoundation

Find the midpoint of (−3,1)(-3, 1) and (5,7)(5, 7).

Exam-style

Question 3Exam-styleFoundation

Find the midpoint of (0,−6)(0, -6) and (−4,2)(-4, 2).

Question 4Exam-styleFoundation

Find the length of the line from (1,2)(1, 2) to (4,6)(4, 6).

Question 5Exam-styleFoundation

Find the length of the line from (−2,3)(-2, 3) to (4,−5)(4, -5).

Question 6Exam-styleFoundation

M(3,5)M(3, 5) is the midpoint of A(1,2)A(1, 2) and BB. Find the coordinates of BB.

Challenge

Question 7ChallengeFoundation

Find the length of the line from (1,1)(1, 1) to (4,3)(4, 3), to 3 significant figures.

Question 8ChallengeHigher

Find the equation of the perpendicular bisector of the line joining (−2,5)(-2, 5) and (4,1)(4, 1).

y =

Common mistakes

  • Subtracting instead of adding for the midpoint.
  • Mixing x and y coordinates.
  • Forgetting the square root at the end of a length.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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