Transformations — Paper 2 · IGCSE Mathematics 0580

17 For y Examiner's Use 8 7 6 5 A 4 3 2 B 1 x 0 1 2 3 4 5 6 7 8 (a) Describe fully the single transformation which maps triangle A onto triangle B. Answer(a) [2] (b) On the grid, draw the image of triangle A after rotation by 90° clockwise about the point (4, 4). [2]

4 marks

Mark scheme: 17 (a) Reflection in y = x 2 M1 Reflection A1 correct description of the line (b) Triangle at (4,6), (4, 7), (7, 7) 2 M1 Rotation 90° clockwise A1 position 3

This question in 0580/21 May/June 2009

20 For y Examiner's Use 9 8 7 6 5 4 M 3 2 1 K L x –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 The triangle KLM is shown on the grid. (a) Calculate angle KML. Answer(a) Angle KML = [2] (b) On the grid, draw the shear of triangle KLM, with a shear factor of 3 and the x-axis invariant. [2]

4 marks

Mark scheme: 4 20 (a) 63.4 2 M1 tan(M) = oe 2 (b) Vertices at (4, 1), (8, 1) and (10, 3) 2 B1 two vertices correct

This question in 0580/23 Oct/Nov 2010

14 y 3 2 A B 1 x 0 1 2 3 4 5 6 7 8 (a) Describe fully the single transformation that maps triangle A onto triangle B. Answer(a) [3] (b) Find the 2 × 2 matrix which represents this transformation.     Answer(b)   [2]    

5 marks

Mark scheme: (c) 14 to 14.5 1

This question in 0580/22 May/June 2012

13 Find the matrix which represents the combined transformation of a reflection in the x axis followed For by a reflection in the line y = x. Examiner's Use     Answer   [3]    

3 marks

Mark scheme: 13  0 − 1 3 M2 for 0 1 1 0 cao 1 0 0 –1  1 0    or B1 for one matrix seen

This question in 0580/21 Oct/Nov 2012

21 For y Examiner's R Use 2 1 P Q x –3 –2 –1 0 1 2 3 –1 –2 The triangle PQR has co-ordinates P(O1, 1), Q(1, 1) and R(1, 2). (a) Rotate triangle PQR by 90° clockwise about (0, 0). Label your image P'Q'R'. [2] (b) Reflect your triangle P'Q'R' in the line y = − x . Label your image P''Q''R''. [2] (c) Describe fully the single transformation which maps triangle PQR onto triangle P''Q''R''. Answer(c) [2]

6 marks

Mark scheme: 21 (a) triangle at (1, 1), (1, –1), (2, –1) 2 SC1 triangle at (–1, –1),(–1, 1), (–2, 1) (b) triangle at (–1, –1)(1, –1), (1, –2) 2ft correct or reflection of their triangle in y = –x (c) reflection in the x axis 2 B1 reflection B1 x axis or y = 0 70

This question in 0580/21 Oct/Nov 2012

17 For y Examiner's Use 3 D C D' C' 2 1 A B A' B' 0 x 1 2 3 4 5 6 7 8 9 A″ B″ –1 –2 D″ C″ (a) Describe the single transformation which maps ABCD onto A' B' C' D'. Answer(a) [3] (b) A single transformation maps A' B' C' D' onto A" B" C" D". Find the matrix which represents this transformation.     Answer(b)   [2]      0 1   0 −1 

5 marks

Mark scheme: 17 (a) Shear x axis invariant sf 3 3 B1 shear B1 x axis invariant oe B1 3  1 0   1 0  k ≠ 0 or k ≠ 1 2 M1   (b)   0 k 0 −1    

This question in 0580/22 Oct/Nov 2012

17 (p, q) is the image of the point (x, y) under this combined transformation. For Examiner′s Use p -1 0 x 3 = + 2 q y f p f 0 1 p f p f p (a) Draw the image of the triangle under the combined transformation. y 4 3 2 1 x 0 –4 –3 –2 –1 1 2 3 4 –1 –2 –3 –4 [3] -1 0 (b) Describe fully the single transformation represented by . f 0 1 p Answer (b) … [2] _____________________________________________________________________________________

5 marks

Mark scheme: 17 (a) triangle at (0, 3) (2, 3) and (2, 4) 3 B1 for each correct vertex If 0 scored then M1 for correct reflection in the y axis or correct translation of their first stage 3 right 2 up (b) reflection in y axis 2 B1 for reflection B1 for y axis or x = 0

This question in 0580/23 Oct/Nov 2013

22 y 7 6 5 4 A 3 2 1 x –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 –2 –3 B –4 –5 –6 3 (a) Draw the image of triangle A after a translation by the vector [2] 4 e - o. (b) Describe fully the single transformation which maps triangle A onto triangle B. Answer(b) … … [3] - 2 0 (c) Draw the image of triangle A after the transformation represented by the matrix [3] e 0 1 o.

8 marks

Mark scheme:     22 (a) Triangle at ( ,2 −1) ( 1,2) (,1 −2 ) 2 B1 for translation by   or    −4   k  (b) Rotation 1 OR enlargement [centre] ( 1, 0 ) 1 [centre] ( 1, 0 ) 180 ° or half turn 1 [scale factor] −1 (c) Triangle at ( 3,2) ( 2,4 ) ( 5,2 ) 3 B2 for 2 correct vertices plotted or If no / wrong plots allow SC2 for 3 correct coordinates shown in working or SC1 for any 2 correct coordinates shown or a triangle of the correct size and orientation but wrong position − 2 0  − 1 − 1 − 2  or M1 for    oe  0 1  3 5 2  shown

This question in 0580/23 May/June 2014

0 1 19 (a) N = f -1 0 p Describe fully the single transformation represented by N. Answer(a) … … [3] (b) Find the matrix which represents the single transformation that maps triangle A onto triangle B. y 7 6 5 4 A 3 2 B 1 x 0 1 2 3 4 5 6 7 8 9 10 Answer(b) [2] f p (c) On the grid, draw the image of triangle A under a stretch, factor 3, with the y-axis invariant. [2]

7 marks

Mark scheme: 19 (a) rotation 3 B1 for each 90 clockwise [about] origin oe  0 1  (b)   2 M1 for any one column or row correct  1 0  (c) Triangle at (3, 3), (6, 3) and (3, 5) 2 M1 for any two vertices correct or correct answer translated horizontally

This question in 0580/23 Oct/Nov 2014

6 Find the 2 × 2 matrix that represents a rotation through 90° clockwise about (0, 0). Answer [2] f p

2 marks

Mark scheme:  0 1  6   2 B1 for one correct column  − 1 0 

This question in 0580/23 May/June 2015

3 y 4 3 2 A 1 x –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 2 Draw the image of shape A after a translation by the vector [2] e - 3 o.__________________________________________________________________________________________

2 marks

Mark scheme: 3 Triangle (3, –2), (4, –2), 2 B1 for movement 2 right or 3 down (4, –1) 785 [ ]

This question in 0580/21 Oct/Nov 2015

17 y 6 5 4 3 S 2 T 1 x 0 1 2 3 4 5 6 7 8 9 (a) Describe fully the single transformation that maps triangle S onto triangle T. Answer(a) … … [3] (b) Find the matrix which represents the transformation that maps triangle S onto triangle T. Answer(b) [2] f p __________________________________________________________________________________________

5 marks

Mark scheme: 17 (a) Enlargement 1 1 1 2 origin oe 1  12 0   k 0  (b) oe 2FT correct or FT their (a) allow for 2 marks      0 k  0 12   where k = their scale factor in (a)  k 0  B1 for one correct row or correct column or    0 k  ( k ≠ 0 or )1  − 9 − 5 

This question in 0580/21 Oct/Nov 2015

18 y 6 5 4 3 B A 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] 1 0 (b) Draw the image of triangle A after the transformation represented by . [3] c0 - 1m

6 marks

Mark scheme: 18 (a) Enlargement 1 1 [s.f.] 1 2 [centre] ( −1 , 3 ) 1 (b) Triangle at (3 ,−1) (5,−1) (5,−5) 3 M2 for 2 correct vertices on grid or in working or M1 for identifying matrix as a reflection in  1 0  3 5 5  the x-axis or for    oe  0 − 1  1 1 5  1  − 4 3   − 4 3 

This question in 0580/22 Oct/Nov 2016

11 y 7 6 5 4 3 2 1 A x 0 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3 - 1 T(X) is the image of the shape X after translation by the vector c 3m. M(Y) is the image of the shape Y after reflection in the line x = 2. On the grid, draw MT(A), the image of shape A after the transformation MT. [3]

3 marks

Mark scheme: 11 3 B2 for correct translation of A seen  −1  k or B1 for translation of A by   or   k  3 seen A and B1 for correct reflection of their translation in x = 2 seen If 0 scored SC2 for correct TM(A) or SC1 for reflection in x = 2 seen or a  −1  correct translation of   seen  3  k

This question in 0580/22 Feb/March 2017

16 y 11 10 9 8 7 A 6 5 4 3 B 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 12 Describe fully the single transformation that maps triangle A onto triangle B. … … [3]

3 marks

Mark scheme: 16 Enlargement 1 1 1 3 (2, 1) 1

This question in 0580/21 Oct/Nov 2017

16 y 7 6 5 4 3 2 1 R x 0 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3 0 - 1 On the grid, draw the image of shape R after the transformation represented by the matrix [3] c1 0m.

3 marks

Mark scheme: 16 Shape with vertices at 3 M2 for 3 correct vertices on grid or in (1, 1), (1, 4), (−1, 2), (−1, 4) working or M1 for correct set-up  0 − 1  2 1 4 4      1 0  1 − 1 − 1 1  or for rotation, 90° [anti-clockwise], centre O

This question in 0580/21 May/June 2018

26 y 10 9 8 7 6 5 U 4 3 T 2 1 x –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 (a) Describe fully the single transformation that maps triangle T onto triangle U. … … [3] (b) On the grid, draw the image of triangle T after a rotation through 90° clockwise about the point (7, 3). [3]

6 marks

Mark scheme: 26(a) Enlargement 3 B1 for each [scale factor] 2 [centre] (7, 0) 26(b) Image at (6, 4), (7, 4), (6, 8) 3 B2 for rotation through 90° clockwise but about other point or B1 for rotation through 90° anticlockwise about any point or for triangle at (6, 4), (7, 4), (6, k)

This question in 0580/23 May/June 2018

0 1 14 Describe fully the single transformation represented by the matrix c1 0m. … … [2]

2 marks

Mark scheme: 14 Reflection 2 B1 for each y = x

This question in 0580/23 Oct/Nov 2018

11 Write down the matrix that represents an enlargement, scale factor 3, centre (0, 0). [2] f p

2 marks

Mark scheme: 11  3 0  2 B1 for one row or one column correct in a   2 by 2 matrix in the final answer  0 3   0 3  or SC1 for    3 0 

This question in 0580/22 May/June 2019

25 y 77 66 55 A 44 33 22 11 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x –1 –2 –3 B C –4 –5 –6 –7 Describe fully the single transformation that maps (a) triangle A onto triangle B, … … [3] (b) triangle A onto triangle C. … … [3]

6 marks

Mark scheme: 25(a) Rotation 3 B1 for each 90° clockwise oe (1, 0) 25(b) Enlargement 3 B1 for each − 2 (0, 2)

This question in 0580/22 May/June 2019

1 2 5 6 19 M = P = e3 4o e7 8o (a) Find MP. [2] f p (b) Find M . … [1]

3 marks

Mark scheme: 19(a)  19 22  2 B1 for 2 or 3 elements correct    43 50  19(b) –2 final answer 1

This question in 0580/21 Oct/Nov 2019

21 y 8 7 T 6 5 4 3 2 A 1 0 x 1 2 3 4 5 6 7 8 (a) Describe fully the single transformation that maps shape T onto shape A. … … [2] (b) On the grid, reflect shape T in the line y = x. [2]

4 marks

Mark scheme: 21(a) Translation 2 B1 for each  − 1     − 5  21(b) Correct reflection at 2 B1 for three correct vertices (6, 2), (6, 6), (7, 6), (7, 3)

This question in 0580/21 Oct/Nov 2019

11 y 7 6 5 4 C 3 2 D 1 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 B – 2 A – 3 – 4 – 5 Describe fully the single transformation that maps (a) shape A onto shape B, … … [3] (b) shape A onto shape C, … … [2] (c) shape A onto shape D. … … [3]

8 marks

Mark scheme: 11(a) Rotation 3 B1 for each 90° clockwise oe (0, 2) 11(b) Reflection 2 B1 for each y = x 11(c) Enlargement 3 B1 for each 1 [sf] 2 (4, 6)

This question in 0580/22 Feb/March 2020

18 y 8 T 6 4 U 2 x 0 2 4 6 8 Describe fully the single transformation that maps triangle T onto triangle U. … … [3]

3 marks

Mark scheme: 18 Enlargement 3 B1 for each 1 [scale factor] − 2 [centre] (3, 4)

This question in 0580/22 May/June 2020

10 y 10 8 6 4 2 C – 8 – 6 – 4 – 2 0 2 4 6 8 10 x – 2 – 4 – 6 A B – 8 – 10 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, … … [3] (ii) triangle A onto triangle C. … … [3] 2 (b) Draw the image of triangle A after a translation by the vector [2] e10o.

8 marks

Mark scheme: 10(a)(i) Rotation 3 B1 for each 90° anticlockwise oe (0, − 1) 10(a)(ii) enlargement 3 B1 for each 1 [s.f.] 3 (6, 6) 10(b) triangle at (− 4, 7) (− 4, 1) (− 1, 1) 2  k  2 B1 for translation by   or   10  k

This question in 0580/21 May/June 2021

10 y 8 6 4 T 2 – 8 – 6 – 4 – 2 0 2 4 6 8 x – 2 – 4 A – 6 – 8 (a) Describe fully the single transformation that maps triangle T onto triangle A. … … [2] 1 (b) Draw the image of triangle T after an enlargement, scale factor - , centre (0, 0). [2] 2

4 marks

Mark scheme: 10(a) Translation 2 B1 for each  − 1     − 8  10(b) Image at (–1, –1), (–4, –1), (–1, –2) 2 B1 for image correct scale factor and orientation but wrong position 1 or for enlargement scale factor centre 2 (0, 0)

This question in 0580/23 May/June 2021

8 y 6 5 4 3 A 2 1 B – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 x – 1 – 2 – 3 – 4 – 5 (a) On the grid, draw the image of (i) triangle A after a reflection in the y-axis, [1] - 3 (ii) triangle A after a translation by the vector [2] e- 4o. (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3]

6 marks

Mark scheme: 8(a)(i) triangle at (− 1, 1) (− 4, 2) (− 3, 5) 1 8(a)(ii) triangle at (− 2, −3) (1, − 2) (0, 1) 2  −3   k  B1 for translation by   or by    k   −4  8(b) enlargement 3 B1 for each 1 [sf] 2 [centre] (9, − 1)

This question in 0580/22 Feb/March 2022

16 y 9 8 T 7 6 5 4 3 P 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 Describe fully the single transformation that maps triangle T onto triangle P. … … [3]

3 marks

Mark scheme: 16 Enlargement 3 B1 for each 1 [sf]  2 [centre] (4, 4)

This question in 0580/21 May/June 2022

14 y 6 5 B 4 3 2 A 1 0 1 2 3 4 5 6 x Describe fully the single transformation that maps triangle A onto triangle B. … … [3]

3 marks

Mark scheme: 14 Rotation 3 B1 for each (5, 3) 90˚ clockwise oe

This question in 0580/21 Oct/Nov 2022

11 y 8 7 6 A 5 B 4 3 2 C 1 – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 x – 1 Describe the single transformation that maps (a) triangle A onto triangle B … … [3] (b) triangle A onto triangle C. … … [3]

6 marks

Mark scheme: 11(a) Enlargement 3 B1 for each [sf] 2 (0, 7) 11(b) Rotation 3 B1 for each (3, 1) 90° clockwise oe

This question in 0580/21 May/June 2023

10 y 10 9 8 7 6 B 5 4 3 2 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 A – 2 – 3 – 4 – 5 – 6 (a) Describe fully the single transformation that maps shape A onto shape B. … … [2] (b) Rotate shape A 90° clockwise about the point ( - 1, 2) . [2] (c) Enlarge shape A by scale factor - 2 , centre (2, 0). [2]

6 marks

Mark scheme: 10(a) Reflection 2 B1 for each y = 2 10(b) Shape at 2 (–2, –2), (–6, –5), (–6, –3), B1 for correct size and orientation but wrong (–4, –2) position or for rotation of 90° anticlockwise about (–1, 2) or for three correct vertices 10(c) Shape at 2 (0, –2), (0, 2), (–2, 6), (–6, 6) B1 for correct size and orientation but wrong position or for three correct vertices

This question in 0580/22 May/June 2023

8 y 5 A 4 3 2 1 – 1 0 1 2 3 4 5 6 7 x – 1 B – 2 – 3 – 4 Describe fully the single transformation that maps triangle A onto triangle B. … … [3]

3 marks

Mark scheme: 8 Rotation 3 B1 for each (0,0) oe 90° clockwise oe

This question in 0580/23 May/June 2023

15 y 4 3 2 1 B A – 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 C – 3 – 4 – 5 – 6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B … … [2] (ii) triangle A onto triangle C. … … [3] (b) Draw the image of triangle A after a rotation, 90° clockwise, about ( 1, 3) . [2]

7 marks

Mark scheme: 15(a)(i) reflection 2 B1 for each x = −2 15(a)(ii) enlargement 3 B1 for each 1 [sf] 2 ( −3, −4 ) 15(b) Image at ( 0, 3 ) , ( −4, 3 ) , ( − 3, −1) 2 B1 for correct size and orientation, wrong centre

This question in 0580/22 Feb/March 2024

9 y 7 6 5 4 B 3 2 A 1 x – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 – 1 – 2 – 3 (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] - 4 (b) On the grid, draw the image of triangle A after a translation by the vector [2] e 3o.

5 marks

Mark scheme: 9(a) Enlargement 3 B1 for each [s f] 2 [centre] 1, 1 9(b) image at  1, 4  1, 5 1, 4  2   4  k B1 for translation by   or   k  3

This question in 0580/22 May/June 2024

19 y 6 T 4 2 – 8 – 6 – 4 – 2 0 2 4 6 8 x – 2 W – 4 – 6 – 8 (a) Describe fully the single transformation that maps triangle T onto triangle W. … … [3] (b) Draw the enlargement of triangle T with scale factor -2 and centre of enlargement ( -1, 1). [2]

5 marks

Mark scheme: 19(a) Rotation 3 B1 for each 90° clockwise oe (0, –2) 19(b) Triangle at 2 B1 for enlargement s.f. –2 in wrong position (–5, –1), (–5, –7), (–7, –7)

This question in 0580/23 May/June 2024

5 y 9 8 7 6 B 5 4 3 A 2 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 11 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (b) On the grid, draw the image of (i) triangle A after a reflection in the line x =-1 [2] (ii) triangle A after a rotation 90° clockwise, centre (1, -2). [2]

7 marks

Mark scheme: 5(a) Enlargement 3 B1 for each [Scale factor] 3 (1, 2) 5(b)(i) Triangle at (–6, 1), (–3, 3), (–4, 4) 2 B1 for reflection in x = k or in y = –1 5(b)(ii) Triangle at (4, –5), (6, –2), (7, –3) 2 B1 for correct 90° anticlockwise rotation about (1, –2) or correct orientation, wrong centre

This question in 0580/23 May/June 2025

5 y 4 3 P 2 T 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 1 – 2 (a) Describe fully the single transformation that maps triangle T onto triangle P. … … [2] (b) Draw the image of triangle T after an enlargement of scale factor 2, centre (3, 3). [2]

4 marks

Mark scheme: 5(a) Translation 2 B1 for each  −3     1  5(b) Triangle at (3, 1) , (3, –1) (–1, –1) 2 B1 for correct size and orientation but wrong position

This question in 0580/21 Oct/Nov 2025