Every transformations question from 19 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 7.1. 19 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/11/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Transformations and Vectors past paper questions.
0580 Transformations past paper questions: Core (Papers 1 and 3)
May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q19
Triangle T has vertices (1, 1), (1, 4) and (2, 1).
(a) Draw the image of triangle T after a translation by the vector (3, −6).
(b) Draw the image of triangle T after a reflection in the line y = −1.
(c) Describe fully the single transformation that maps triangle T onto triangle A.
(d) Describe fully the single transformation that maps triangle T onto triangle B.
Show solution
- The vector (3, −6) means 3 right and 6 down. Add 3 to each x and subtract 6 from each y.
- (1, 1) → (4, −5), (1, 4) → (4, −2), (2, 1) → (5, −5).
- (4, −5), (4, −2), (5, −5)
- y = −1 is a horizontal line. Each point moves to the same distance on the other side of it.
- (1, 1) is 2 above the line, so it goes 2 below: (1, −3). (1, 4) is 5 above, so (1, −6). (2, 1) → (2, −3).
- (1, −3), (1, −6), (2, −3)
- A is the same shape as T but twice as big, so it is an enlargement, scale factor 2.
- Draw straight lines through matching corners of T and A. They all meet at the centre, (5, 4).
- Enlargement, scale factor 2, centre (5, 4)
- B is the same size as T but turned, so it is a rotation.
- Matching corners: (1, 4) → (4, −1), (1, 1) → (1, −1), (2, 1) → (1, −2). Each (x, y) becomes (y, −x).
- (x, y) → (y, −x) is a quarter-turn clockwise about the origin.
- Rotation, 90° clockwise, centre (0, 0)
May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q29
The diagram shows three shapes, A, B and C, on a grid.
(a) Describe fully the single transformation that maps (i) shape A onto shape B (ii) shape B onto shape C.
(b) Draw the image of shape A after a translation by the vector (1, −3).
Show solution
- A and B are the same size but flipped, so it is a reflection.
- Each corner of A is the same distance from the vertical line halfway between the shapes as its matching corner of B.
- Reflection in the line x = −0.5
- C is the same size as B but turned a quarter-turn clockwise, so it is a rotation.
- Use tracing paper to find the point that stays fixed: (2, 4).
- Rotation, 90° clockwise, centre (2, 4)
- The vector (1, −3) means 1 right and 3 down. Add 1 to each x and subtract 3 from each y.
- (−2, 1), (−4, 1), (−3, 0), (−5, −2), (−3, −2)
May/June 2026 · Paper 1 · 0580/13/M/J/26 · Q20
Triangle A has vertices (2, 2), (4, 2) and (3, 6).
(a) Describe fully the single transformation that maps triangle A onto triangle B.
(b) Describe fully the single transformation that maps triangle A onto triangle C.
(c) Draw the image of shape A after a rotation of 180°, centre (0, 0).
Show solution
- B is the same size and the same way round as A, so it is a translation.
- Compare matching corners: the top corner moves from (3, 6) to (5, −1). That is 2 right and 7 down.
- Translation by the vector (2, −7)
- C is the same shape as A but half the size, so the scale factor is 1⁄2.
- Each corner of C is halfway between the origin and the matching corner of A, for example (3, 6) → (1.5, 3).
- Enlargement, scale factor 1⁄2, centre (0, 0)
- A rotation of 180° about (0, 0) changes the sign of both coordinates: (x, y) → (−x, −y).
- (2, 2) → (−2, −2), (4, 2) → (−4, −2), (3, 6) → (−3, −6).
- (−2, −2), (−4, −2), (−3, −6)
Feb/Mar 2026 · Paper 1 · 0580/12/F/M/26 · Q21
The diagram shows two triangles, A and B, on a 1 cm² grid. Triangle A has vertices (−2, 1), (7, 4) and (4, 10). Triangle B has vertices (−4, 1), (−1, 2) and (−2, 4).
(a) Describe fully the single transformation that maps triangle A onto triangle B.
(b) On the grid, draw the image of triangle B after a rotation of 180°, centre (−2, 4).
(c) Triangle A is reflected in the line x = 7. Work out the coordinates of the vertices of triangle A after this reflection.
Show solution
- B is the same shape as A but smaller, so it is an enlargement.
- Match the corners: (−2, 1) → (−4, 1), (7, 4) → (−1, 2), (4, 10) → (−2, 4). Each length in B is 1⁄3 of the length in A, so the scale factor is 1⁄3.
- Draw lines through matching corners. They meet at the centre, (−5, 1).
- Check: (7, 4) is 12 right and 3 up from (−5, 1). One third of that is 4 right and 1 up, which lands on (−1, 2) ✓
- Enlargement, scale factor 1⁄3, centre (−5, 1)
- A rotation of 180° sends each point to the same distance on the opposite side of the centre (−2, 4).
- (−4, 1) is 2 left and 3 down from the centre, so it goes 2 right and 3 up: (0, 7).
- (−1, 2) is 1 right and 2 down, so it goes 1 left and 2 up: (−3, 6). The corner (−2, 4) is the centre and stays put.
- (−3, 6), (−2, 4), (0, 7)
- The mirror line x = 7 is vertical. Each point keeps its y-value and moves to the same distance on the other side.
- (−2, 1) is 9 left of the line, so it goes 9 right: (16, 1). (7, 4) is on the line and stays. (4, 10) is 3 left, so it goes 3 right: (10, 10).
- (7, 4), (16, 1), (10, 10)
Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q21
Shape A is a rectangle with vertices (1, 1), (3, 1), (3, 2) and (1, 2). Shape B is shown on the grid.
(a) Describe fully the single transformation that maps shape A onto shape B.
(b) Draw the image of shape A after a reflection in the line y = −1.
Show solution
- B is the same size as A but turned, so it is a rotation.
- Matching corners: (1, 1) → (−1, 1), (3, 1) → (−1, 3), (3, 2) → (−2, 3). Each (x, y) becomes (−y, x).
- (x, y) → (−y, x) is a quarter-turn anticlockwise about the origin.
- Rotation, 90° anticlockwise, centre (0, 0)
- y = −1 is a horizontal line. Each corner moves to the same distance on the other side.
- (1, 1) and (3, 1) are 2 above the line, so they go to y = −3. (3, 2) and (1, 2) are 3 above, so they go to y = −4.
- (1, −3), (3, −3), (3, −4), (1, −4)
Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q19
The grid shows two flags, F and A. Flag F has vertices (2, 5), (3, 5), (3, 4), (2, 4) and (2, 2).
(a) Draw the image of flag F after a reflection in the line x = −1.
(b) Draw the image of flag F after a rotation of 180° about (0, 0).
(c) Describe fully the single transformation that maps flag F onto flag A.
Show solution
- x = −1 is a vertical mirror line. Each point keeps its y-value and moves to the same distance on the other side.
- (2, 5) is 3 right of the line, so it goes 3 left: (−4, 5). Do the same for every corner.
- (−4, 5), (−5, 5), (−5, 4), (−4, 4), (−4, 2)
- A rotation of 180° about (0, 0) changes the sign of both coordinates: (x, y) → (−x, −y).
- (−2, −5), (−3, −5), (−3, −4), (−2, −4), (−2, −2)
- A is the same size and the same way round as F, so it is a translation.
- F’s bottom corner (2, 2) matches A’s bottom corner (4, −4): that is 2 right and 6 down.
- Translation by the vector (2, −6)
Oct/Nov 2025 · Paper 1 · 0580/13/O/N/25 · Q22
The diagram shows triangles A and B. Describe fully the single transformation that maps triangle A onto triangle B.
Show solution
- B is the same shape as A, but each side is 3 times as long, so the scale factor is 3.
- Draw lines through matching corners of A and B. They all meet at the origin.
- Enlargement, scale factor 3, centre (0, 0)
Oct/Nov 2025 · Paper 3 · 0580/31/O/N/25 · Q15
Shape A is a triangle with vertices (−4, −5), (−2, −5) and (−4, −2). Shape B is shown on the grid.
(a) Describe fully the single transformation that maps shape A onto shape B.
(b) Draw the image of shape A after a translation by the vector (6, 7).
Show solution
- B is the same shape as A but half the size, so the scale factor is 0.5.
- Each corner of B is halfway between the origin and the matching corner of A, for example (−4, −2) → (−2, −1).
- Enlargement, scale factor 0.5, centre (0, 0)
- The vector (6, 7) means 6 right and 7 up. Add 6 to each x and 7 to each y.
- (−4, −5) → (2, 2), (−2, −5) → (4, 2), (−4, −2) → (2, 5).
- (2, 2), (4, 2), (2, 5)
Oct/Nov 2025 · Paper 3 · 0580/33/O/N/25 · Q21
Shape A has vertices (−4, 2), (−2, 2), (−1, 3) and (−3, 3). Shape B is shown on the grid.
(a) Describe fully the single transformation that maps shape A onto shape B.
(b) On the grid, draw the image of shape A after a reflection in the line y = 0.
Show solution
- Compare a corner of A with the matching corner of B. Each point (x, y) of A moves to (y, −x).
- That is a quarter-turn clockwise about the origin.
- Rotation, 90° clockwise, centre (0, 0)
- Tip: To describe a rotation fully, give all three: the angle, the direction and the centre.
- The line y = 0 is the x-axis. Reflecting in it keeps x the same and changes the sign of y.
- (−4, 2) → (−4, −2), (−2, 2) → (−2, −2), (−1, 3) → (−1, −3), (−3, 3) → (−3, −3).
- Draw the shape with corners (−4, −2), (−2, −2), (−1, −3), (−3, −3)
May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q23
Triangle T has vertices (1, 1), (1, 3) and (4, 1). Triangles A and B are also drawn on the grid.
(a) On the grid, draw the image of triangle T after a rotation, 90° clockwise, centre (0, 0).
(b) Describe fully the single transformation that maps triangle T onto triangle A.
(c) Describe fully the single transformation that maps triangle T onto triangle B.
Show solution
- Rotating 90° clockwise about (0, 0) sends a point (x, y) to (y, −x).
- (1, 1) → (1, −1), (1, 3) → (3, −1), (4, 1) → (1, −4).
- The image has vertices (1, −1), (3, −1) and (1, −4).
- A is the same size and the same way round as T, so it is a translation.
- Compare matching corners: T’s corner (1, 1) moves to A’s corner (−5, −3). That is 6 left and 4 down.
- Translation by the vector (−6, −4)
- B is the same shape but its sides are twice as long, so it is an enlargement with scale factor 2.
- Draw lines through matching corners of T and B. They meet at the centre, (0, −2).
- Enlargement, scale factor 2, centre (0, −2)
May/June 2025 · Paper 1 · 0580/12/M/J/25 · Q16
The diagram shows a point P and three triangles, A, B and C, on a 1 cm² grid. Triangle A has vertices (1, 0), (2, 0) and (2, 3).
(a) Find the area of triangle B.
(b)(i) Write down the coordinates of point P.
(b)(ii) Work out the coordinates of point P after a translation by the vector (−20, 12).
(c) Draw the image of triangle A after a reflection in the line y = −1.
(d) Describe fully the single transformation that maps (i) triangle A onto triangle B (ii) triangle A onto triangle C.
Show solution
- Triangle B has a horizontal base from x = 3 to x = 5, so the base is 2 cm.
- Its height goes from y = 0 to y = 6, so the height is 6 cm.
- Area = 1⁄2 × base × height = 1⁄2 × 2 × 6 = 6 cm²
- Read across to P, then up or down: P = (4, −3)
- The vector (−20, 12) means 20 left and 12 up.
- x: 4 − 20 = −16. y: −3 + 12 = 9.
- P moves to (−16, 9)
- y = −1 is a horizontal mirror line. Each point keeps its x-value and moves to the same distance on the other side.
- (1, 0) is 1 above the line, so it goes to (1, −2). (2, 0) → (2, −2). (2, 3) is 4 above, so it goes to (2, −5).
- The image has vertices (1, −2), (2, −2) and (2, −5).
- B is the same shape as A but twice as big, so it is an enlargement with scale factor 2.
- Draw lines through matching corners, for example (2, 3) to (5, 6) and (1, 0) to (3, 0). They meet at (−1, 0).
- Enlargement, scale factor 2, centre (−1, 0)
- C is the same size as A but turned a quarter-turn clockwise, so it is a rotation.
- The corner (2, 3) stays in the same place on both triangles, so it is the centre.
- Rotation, 90° clockwise, centre (2, 3)
0580 Transformations past paper questions: Extended (Papers 2 and 4)
May/June 2026 · Paper 2 · 0580/21/M/J/26 · Q17
Shape A has vertices (2, 7), (6, 9), (8, 5) and (4, 5).
(a) Draw the image of shape A after a reflection in the line x = 1.
(b) Describe fully the single transformation that maps shape A onto shape B.
Show solution
- x = 1 is a vertical mirror line. Each point keeps its y-value and moves the same distance to the other side.
- For a point at x, the distance to the line is x − 1, so the image is at 1 − (x − 1) = 2 − x.
- (2, 7) → (0, 7), (6, 9) → (−4, 9), (8, 5) → (−6, 5), (4, 5) → (−2, 5).
- (0, 7), (−4, 9), (−6, 5), (−2, 5)
- B is half the size of A and upside down, so it is an enlargement with a negative scale factor, −1⁄2.
- Join matching corners of A and B. The lines cross at the centre (2, −1).
- Check with one corner: (6, 9) is 4 right and 10 up from (2, −1). Multiply by −1⁄2: 2 left and 5 down, which lands on (0, −6), a corner of B ✓
- Enlargement, scale factor −1⁄2, centre (2, −1)
May/June 2026 · Paper 2 · 0580/22/M/J/26 · Q5
Shape A has vertices (−4, 2), (−2, 2), (−2, 0) and (−3, 0).
(a) Draw the image of (i) shape A after a translation by the vector (−2, 5) (ii) shape A after a reflection in the line y = x.
(b) Describe fully the single transformation that maps shape A onto shape B.
Show solution
- The vector (−2, 5) means 2 left and 5 up. Subtract 2 from each x and add 5 to each y.
- (−4, 2) → (−6, 7), (−2, 2) → (−4, 7), (−2, 0) → (−4, 5), (−3, 0) → (−5, 5).
- (−6, 7), (−4, 7), (−4, 5), (−5, 5)
- Reflecting in the line y = x swaps the coordinates: (x, y) → (y, x).
- (−4, 2) → (2, −4), (−2, 2) → (2, −2), (−2, 0) → (0, −2), (−3, 0) → (0, −3).
- (2, −4), (2, −2), (0, −2), (0, −3)
- B is the same size as A but turned a quarter-turn anticlockwise, so it is a rotation.
- Use tracing paper to find the centre: (3, 3).
- Check: (−4, 2) is 7 left and 1 down from (3, 3). A quarter-turn anticlockwise makes this 1 right and 7 down, landing on (4, −4), a corner of B ✓
- Rotation, 90° anticlockwise, centre (3, 3)
May/June 2026 · Paper 2 · 0580/23/M/J/26 · Q12
Triangle A has vertices (1, −4), (2, −4) and (2, −2).
(a) Describe fully the single transformation that maps (i) triangle A onto triangle B (ii) triangle A onto triangle C.
(b) On the grid, draw the image of (i) triangle A after a reflection in the y-axis (ii) triangle A after a translation by the vector (−1, 3).
Show solution
- B is the same size as A but turned, so it is a rotation.
- Test (x, y) → (−y, x), which is a quarter-turn anticlockwise about the origin.
- (1, −4) → (4, 1), (2, −4) → (4, 2), (2, −2) → (2, 2). These are the corners of B ✓
- Rotation, 90° anticlockwise, centre (0, 0)
- C is twice the size of A and upside down, so it is an enlargement with a negative scale factor, −2.
- Join matching corners of A and C. The lines cross at the centre, (0, −2).
- Check: (1, −4) is 1 right and 2 down from (0, −2). Multiply by −2: 2 left and 4 up, landing on (−2, 2), a corner of C ✓
- Enlargement, scale factor −2, centre (0, −2)
- Reflecting in the y-axis changes the sign of each x-coordinate: (x, y) → (−x, y).
- (−1, −4), (−2, −4), (−2, −2)
- The vector (−1, 3) means 1 left and 3 up. Subtract 1 from each x and add 3 to each y.
- (0, −1), (1, −1), (1, 1)
Feb/Mar 2026 · Paper 2 · 0580/22/F/M/26 · Q11
Triangle A has vertices (−2, 1), (0, 1) and (−2, 4).
(a) On the grid, draw the image of (i) triangle A after a translation by the vector (−3, −5) (ii) triangle A after a reflection in the line y = x.
(b) Describe fully the single transformation that maps triangle A onto triangle B.
Show solution
- The vector (−3, −5) means 3 left and 5 down. Subtract 3 from each x and 5 from each y.
- (−2, 1) → (−5, −4), (0, 1) → (−3, −4), (−2, 4) → (−5, −1).
- (−5, −4), (−3, −4), (−5, −1)
- Reflecting in the line y = x swaps the x and y coordinates: (x, y) → (y, x).
- (−2, 1) → (1, −2), (0, 1) → (1, 0), (−2, 4) → (4, −2).
- (1, −2), (1, 0), (4, −2)
- B is the same size as A but turned, so it is a rotation. Compare the triangles to see it has turned a quarter-turn clockwise.
- Use tracing paper, or test points, to find the centre: (−1, 5).
- Check: (−2, 1) is 1 left and 4 down from (−1, 5). A quarter-turn clockwise makes this 4 left and 1 up, landing on (−5, 6), a corner of B ✓
- Rotation, 90° clockwise, centre (−1, 5)
Oct/Nov 2025 · Paper 2 · 0580/21/O/N/25 · Q5
Triangle T has vertices (1, 1), (3, 1) and (3, 2). Triangle P is shown on the grid.
(a) Describe fully the single transformation that maps triangle T onto triangle P.
(b) Draw the image of triangle T after an enlargement of scale factor 2, centre (3, 3).
Show solution
- P is the same size and the same way round as T, so it is a translation.
- Compare matching corners: T’s corner (1, 1) moves to P’s corner (−2, 2). That is 3 left and 1 up.
- Translation by the vector (−3, 1)
- For an enlargement, find how far each corner is from the centre (3, 3), then double that distance.
- (3, 2) is 1 down from the centre, so its image is 2 down: (3, 1).
- (3, 1) is 2 down, so its image is 4 down: (3, −1).
- (1, 1) is 2 left and 2 down, so its image is 4 left and 4 down: (−1, −1).
- (3, 1), (3, −1), (−1, −1)
Oct/Nov 2025 · Paper 4 · 0580/42/O/N/25 · Q8
Shape A has vertices (−3, 4), (−4, 5), (−5, 5) and (−4, 3). Shape B is shown on the grid.
(a) Draw the image of (i) shape A after a translation by the vector (1, −7) (ii) shape A after a reflection in the line y = x + 1.
(b) Describe fully the single transformation that maps shape A onto shape B.
Show solution
- The vector (1, −7) means 1 right and 7 down. Add 1 to each x and subtract 7 from each y.
- (−3, 4) → (−2, −3), (−4, 5) → (−3, −2), (−5, 5) → (−4, −2), (−4, 3) → (−3, −4).
- Draw the shape with corners (−2, −3), (−3, −2), (−4, −2), (−3, −4)
- First draw the mirror line y = x + 1, through (0, 1) and (2, 3).
- Reflecting in y = x + 1 sends each point (x, y) to (y − 1, x + 1).
- (−3, 4) → (3, −2), (−4, 5) → (4, −3), (−5, 5) → (4, −4), (−4, 3) → (2, −3).
- Draw the shape with corners (3, −2), (4, −3), (4, −4), (2, −3)
- B is the same size as A but turned a quarter-turn. Use tracing paper to find the centre that works.
- Rotation, 90° anticlockwise, centre (−2, 6)
- Tip: A full description of a rotation needs the angle, the direction and the centre.
Oct/Nov 2025 · Paper 4 · 0580/43/O/N/25 · Q7
Triangles D, E and F are drawn on a grid.
(a) Describe fully the single transformation that maps triangle D onto triangle E.
(b) Describe fully the single transformation that maps triangle D onto triangle F.
Show solution
- E is the same size as D and faces the same way, so it is a translation.
- Pick one corner of D and the matching corner of E, and count the squares: 2 right and 8 down.
- Translation by the vector (2, −8)
- F is smaller than D and upside down, so it is an enlargement with a negative scale factor.
- Compare matching sides: each side of F is one third of the length of D’s, so the scale factor is −1⁄3.
- Draw lines through matching corners of D and F. They all cross at (−3, 4), which is the centre.
- Enlargement, scale factor −1⁄3, centre (−3, 4)
May/June 2025 · Paper 2 · 0580/22/M/J/25 · Q5
Triangle T has vertices (−1, 1), (−1, 3) and (−2, 1). Triangle U is also drawn on the grid.
(a) Translate triangle T by the vector (0, −2).
(b) Describe fully the single transformation that maps triangle T onto triangle U.
Show solution
- The vector (0, −2) means 0 across and 2 down. Subtract 2 from each y-coordinate.
- (−1, 1) → (−1, −1), (−1, 3) → (−1, 1), (−2, 1) → (−2, −1).
- (−1, −1), (−1, 1) and (−2, −1)
- U is the same size as T but turned a quarter-turn anticlockwise, so it is a rotation.
- Use tracing paper: trace T, put a pencil point on a guess for the centre and turn 90° anticlockwise until T lands on U. The centre is (2, 2).
- Check: (−1, 1) is 3 left and 1 down from (2, 2). A quarter-turn anticlockwise makes this 1 right and 3 down, landing on (3, −1), a corner of U ✓
- Rotation, 90° anticlockwise, centre (2, 2)
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