Transformations: Edexcel 4MA1 Past Paper Questions and Worked Solutions
This page collects every transformations question from the Pearson Edexcel International GCSE Mathematics A (4MA1) Higher tier Paper 1H and Paper 1HR, January 2020 to June 2025: 3 questions worth 12 marks. Questions run from easier to harder. Try each one first, then click “Show solution” for a step-by-step method with the reason for every step. All answers are checked against the official Pearson mark schemes.
The diagram shows a sketch of triangle A and triangle B on a coordinate grid. Triangle A has vertices (−7, 2), (−11, −5) and (f, −3). Triangle B has vertices (6, 12), (2, d) and (9, e).
(a) Given that triangle A has been translated to give triangle B, work out the value of d, the value of e and the value of f. (3)
The diagram also shows shape P with vertices (2, 5), (2, 3), (3, 2), (3, 3) and shape Q with vertices (6, 11), (6, 5), (9, 2), (9, 5).
(b) Describe fully the single transformation that maps shape P onto shape Q. (3)
(c) Rotate shape P 90° clockwise about (3, 5). Label your shape R. (2)
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Part (a)
- The top vertex (−7, 2) moves to (6, 12). That is 13 right and 10 up, so the translation is 13 units right and 10 units up.
- (−11, −5) moves to (−11 + 13, −5 + 10) = (2, 5), so d = 5
- (f, −3) moves to (9, e): f + 13 = 9 gives f = −4, and −3 + 10 = 7 gives e = 7
Answer: d = 5, e = 7, f = −4
Part (b)
- Q is bigger than P, so it is an enlargement.
- The vertical side of P from (2, 3) to (2, 5) is 2 long. The matching side of Q from (6, 5) to (6, 11) is 6 long.
- Scale factor = 6 ÷ 2 = 3
- To find the centre, draw lines through matching vertices, for example (2, 5) to (6, 11) and (3, 2) to (9, 2). They meet at (0, 2).
- Check: from (0, 2) to (3, 2) is 3 across; × 3 = 9 across, giving (9, 2) ✓
Answer: Enlargement, scale factor 3, centre (0, 2)
Part (c)
- For a 90° clockwise turn about (3, 5), each point’s position relative to the centre changes from (across, up) to (up, −across).
- (2, 5) → (3, 6), (2, 3) → (1, 6), (3, 2) → (0, 5), (3, 3) → (1, 5)
Answer: R has vertices (3, 6), (1, 6), (0, 5) and (1, 5)
The shaded shape has vertices (7, 10), (15, 10), (15, 4) and (11, 4). On the grid, enlarge the shaded shape with scale factor 12 and centre (1, 2).
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- For each vertex, halve its distance from the centre (1, 2).
- (7, 10) is 6 right and 8 up from (1, 2). Half: 3 right and 4 up, giving (4, 6).
- (15, 10) is 14 right and 8 up. Half: 7 right and 4 up, giving (8, 6).
- (15, 4) is 14 right and 2 up. Half: 7 right and 1 up, giving (8, 3).
- (11, 4) is 10 right and 2 up. Half: 5 right and 1 up, giving (6, 3).
Answer: Shape with vertices (4, 6), (8, 6), (8, 3) and (6, 3)
The shaded triangle has vertices (7, 4), (13, 4) and (7, 13). On the grid, enlarge the shaded shape with scale factor 13 and centre (1, 7).
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- For each vertex, find how far it is from the centre (1, 7), multiply that distance by 13, and measure it from the centre again.
- (7, 4) is 6 right and 3 down from (1, 7). A third of that is 2 right and 1 down, giving (3, 6).
- (13, 4) is 12 right and 3 down. A third: 4 right and 1 down, giving (5, 6).
- (7, 13) is 6 right and 6 up. A third: 2 right and 2 up, giving (3, 9).
Answer: Triangle with vertices (3, 6), (5, 6) and (3, 9)
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