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Midpoint of a line segment

Free Printable Midpoint of a line segment PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free midpoint of a line segment worksheets (PDF), GCSE maths past paper questions and worked solutions for Midpoint of a line segment (5P). This is a Grade 5 algebra topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Corbett Maths, Maths Made Easy, M4ths.com, GCSE Maths Rocket, Dr Austin, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our midpoint of a line segment revision notes and worked examples with diagrams, try real GCSE past paper midpoint of a line segment questions with step-by-step solutions, or download a PDF of all midpoint of a line segment worksheet links.

Free Midpoint of a line segment PDF Worksheets & Answers

Grade 5 • Topic 5P
Resource Questions Answers
Practice Questions & answers
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Textbook Exercise & answers
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MME worksheet & model answers
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GCSE worksheet & answers
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Practice questions & answers
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Practice grid / worksheet & answers
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
AQA GCSE topic questions & solutions
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PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
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Interactive online lesson & practice
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Self-marking online worksheet
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Grade 5 topics
5A - Combining ratios5B - Direct and inverse proportion
5C - Reverse percentages5D - Standard form
5E - Speed5F - Changing the subject
5G - Quadratic expressions5H - Solving quadratic equations
5J - Drawing quadratic graphs5K - Cubic/reciprocal graphs
5L - Simultaneous equations5M - Sector areas and arc lengths
5N - Sim. equ. graphically5P - Midpoint of a line segment
5Q - Gradient of a line5R - Equation of a line
5S - Spheres and cones5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)5V - Exact trig. values
5W - Probability trees5X - Vectors
5Y - Venn diagrams5Z - Density
5AA - Pressure
GCSE Maths Grade 5 Revision Notes & Method

Guide to Midpoint of a line segment: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

The midpoint M of a line segment joining (x1, y1) and (x2, y2) is halfway between the two points. Find it by working out the mean (average) of the x-coordinates and the mean of the y-coordinates: M = (x1 + x22, y1 + y22).

If you are given one endpoint and the midpoint and asked to find the other endpoint, find the step from the known endpoint to the midpoint and add that same step again.

Example 1: Find the coordinates of the midpoint of the line segment joining A(−3, 8) and B(7, −2).

Solution:

xM = −3 + 72 = 42 = 2
yM = 8 + (−2)2 = 62 = 3
Answer: (2, 3)
A(−3,8) M(2,3) B(7,−2)

Example 2: M(4, −1) is the midpoint of line PQ. Given that P is (1, 5), find the coordinates of Q.

Solution:

x-step from P to M: 1 → 4 is +3, so xQ = 4 + 3 = 7
y-step from P to M: 5 → −1 is −6, so yQ = −1 − 6 = −7
Answer: Q(7, −7)
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Midpoint of a line segment Questions & Answers

Past Paper Example 1 IGCSE Jan 2022 2F Q5 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows points A and B marked on a grid of squares.
yxO−5−4−3−2−11234567−3−2−1123456AB
(a) On the grid, draw the line with equation y = -2 [1 mark]
(b) Find the coordinates of M [2 marks]
(c) Find the value of d [1 mark]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Horizontal line through (0, –2) B1
Answer (a): Horizontal line drawn at y = −2
Part (b) Solution:
((–3 + 1)/2, (1 + 3)/2) = (–1, 2) M1 A1
Answer (b): (-1, 2)
Part (c) Solution:
AB² = 4² + 2² = 20
for BD = AB with xD = 5 (4 units right of B), yD = 3 – 2 = 1 ⇒ d = 1 B1
Answer (c): d = 1
Past Paper Example 2 IGCSE Jun 2024 1FR Q9 5 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows three points, A, B and C, marked on a grid.
xyO−5−4−3−2−112345−4−3−2−11234ABC
(a) Write down the coordinates of A [1 mark]
(b) Find the coordinates of the midpoint of AB [2 marks]
(c) Find the coordinates of D [2 marks]
Worked Solution & Mark Scheme (5 marks)
Part (a) Solution:
A = (−4, 2) B1
Answer (a): −4, 2
Part (b) Solution:
Midpoint = ((−4+2)/2, (2+4)/2) = (−1, 3) M1 A1
Answer (b): −1, 3
Part (c) Solution:
D = A + (C − B) = (−4 + 1, 2 − 3) = (−3, −1) M1 A1
Answer (c): −3, −1
Past Paper Example 3 IGCSE Jun 2025 2F Q5 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows three points, P, Q and R, marked on a grid.
xy–4–3–2–11234–3–2–112345OPQR
(a) Write down the coordinates of point P [1 mark]
(b) On the grid, mark with a cross (×) the point with coordinates (3, -1)
Label this point T [1 mark]
(c) Find the coordinates of the midpoint of QR [2 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
(–2, 3) B1
Answer (a): –2, 3
Part (b) Solution:
Point T marked at (3, –1)
Answer (b): Point T marked at (3, –1)
Part (c) Solution:
Midpoint of (3, 4) and (1, –2) = ((3 + 1)/2, (4 + –2)/2) = (2, 1) M1 A1
Answer (c): 2, 1

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