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Midpoint of a line segment Quiz

Grade 5 • 5P • 10 Questions (27 Marks)

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Score: 0 / 10
Midpoint of a line segment — Notes & Worked Examples Show / Hide

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)
Question 1 AQA Nov 2023 1H Q3
[1 mark]
A is (2, 0) and B is (0, -4)
Work out the midpoint of AB.
Answer
Worked Solution & Answer
Midpoint = ((2 + 0)/2, (0 + –4)/2) = (1, –2). B1
Answer: Answer (1, –2)
Question Paper (PDF) • Mark Scheme (PDF)
Question 2 AQA Nov 2019 1H Q3
[1 mark]
A is (2, 13) and B is (10, 1)
Circle the midpoint of AB.
(4, 6) (5, 6.5) (6, 7) (8, 12)
Worked Solution & Answer
Midpoint = (2 + 102, 13 + 12) = (122, 142) = (6, 7). B1
Answer: (6, 7)
Question Paper (PDF) • Mark Scheme (PDF)
Question 3
[2 marks]
xy–5–4–3–2–112345–5–4–3–2–112345OPQ
Find the coordinates of the midpoint of PQ where P = (–3, –2) and Q = (2, 4).
Find the coordinates of the midpoint of PQ.
Worked Solution & Answer
((–3 + 2)/2, (–2 + 4)/2) = (–0.5, 1) M1 A1
Answer: (–0.5, 1)
Question Paper (PDF) • Mark Scheme (PDF)
Question 4
[2 marks]
xy–4–3–2–11234–4–3–2–11234OBC
Work out
(a) Plot the point with coordinates (3, 2) and label it A. (1) (b) Write down the coordinates of the midpoint of BC. (1)
(a) Plot the point with coordinates (3, 2)
Label this point A. [1 mark]
(b) Write down the coordinates of the midpoint of BC. [1 mark]
Worked Solution & Answer
(a)
Point A plotted at (3, 2)
Answer (a): Point A plotted at (3, 2)
(b)
Midpoint of (–3, 2) and (1, –2) is ((–3 + 1)/2, (2 + –2)/2) = (–1, 0) B1
Answer (b): –1, 0
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 AQA Jun 2025 3F Q2
[2 marks]
Line AB is on a grid.
012345678912345678xyAB
(a) Write down the coordinates of B. [1 mark]
Answer
(b) Write down the coordinates of the midpoint of the line AB. [1 mark]
Answer
Worked Solution & Answer
(a)
Point B is at x = 8, y = 1: (8, 1) B1
Answer (a): Answer 8, 1
(b)
Midpoint x = (8 + 8)/2 = 8, y = (7 + 1)/2 = 4: (8, 4) B1
Answer (b): Answer 8, 4
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 AQA Nov 2023 3F Q6
[2 marks]
Here is a right-angled triangle on a centimetre grid.
012345678912345xy
(a) Write down the coordinates of the midpoint of the longest side. [1 mark]
(b) Work out the area of the triangle. [1 mark]
Answer cm²
Worked Solution & Answer
(a)
The endpoints of the hypotenuse are (1, 5) and (9, 1)
Midpoint = (1+92, 5+12) = (5, 3). B1
Answer (a): (5, 3)
(b)
(The area of a triangle is ½ × base × height)
Base = 8 cm, height = 4 cm.
Area = 12 × 8 × 4 = 16 cm2. B1
Answer (b): Answer 16 cm²
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 IGCSE Jan 2022 2F Q5
[4 marks]
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]
d =
Worked Solution & Answer
(a)
Horizontal line through (0, –2) B1
Answer (a): Horizontal line drawn at y = −2
(b)
((–3 + 1)/2, (1 + 3)/2) = (–1, 2) M1 A1
Answer (b): (-1, 2)
(c)
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
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 IGCSE Jun 2025 2F Q5
[4 marks]
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 & Answer
(a)
(–2, 3) B1
Answer (a): –2, 3
(b)
Point T marked at (3, –1)
Answer (b): Point T marked at (3, –1)
(c)
Midpoint of (3, 4) and (1, –2) = ((3 + 1)/2, (4 + –2)/2) = (2, 1) M1 A1
Answer (c): 2, 1
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 IGCSE Jan 2020 1F Q14 / 1H Q1
[4 marks]
The point A has coordinates (5, -4)
The point B has coordinates (13, 1)
(a) Work out the coordinates of the midpoint of AB. [2 marks]
(b) Write down the gradient of line L. [1 mark]
(c) Does the point with coordinates (100, -302) lie on line L?
You must give a reason for your answer. [1 mark]
Worked Solution & Answer
(a)
((5+13)/2, (−4+1)/2) = (9, −1.5) M1 A1
Answer (a): 9, -1.5
(b)
m = −3
Answer (b): -3
(c)
y = 2 − 3(100) = −298 ≠ −302 B1
Answer (c): No, because when x = 100, y = 2 − 3(100) = −298 ≠ −302
Question Paper (PDF) • Mark Scheme (PDF)
Question 10 IGCSE Jun 2024 1FR Q9
[5 marks]
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 & Answer
(a)
A = (−4, 2) B1
Answer (a): −4, 2
(b)
Midpoint = ((−4+2)/2, (2+4)/2) = (−1, 3) M1 A1
Answer (b): −1, 3
(c)
D = A + (C − B) = (−4 + 1, 2 − 3) = (−3, −1) M1 A1
Answer (c): −3, −1
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 27 marks)
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Grade 5 Quizzes

25 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