Transformations: IGCSE Mathematics questions with answers
Free Transformations questions for IGCSE Mathematics (0580), part of Transformations & vectors. Each question has the answer and the marking points an examiner would look for.
The point Q(−1, −3) is mapped onto Q′ by a rotation of 180° about the origin. Q′ is then mapped onto Q″ by a reflection in the y-axis. Find the coordinates of Q″.
[2]
(b)
Describe fully the single transformation that maps any point onto its final image under these two transformations combined.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
(−1, 3)
Q′ = (1, 3) B1 (−1, 3) B1
2
(b)
A reflection in the x-axis
reflection B1 the x-axis B1 full description, no extra transformations B1
3
Question 2Structured · 12 marksA* challenge
E1 is the enlargement with centre (0, 0) and scale factor 2. E2 is the enlargement with centre (6, 0) and scale factor −12. Triangle T has vertices (1, 1), (3, 1) and (1, 4).
(a)
T is transformed by E1 and then the image is transformed by E2. Find the coordinates of the vertices of the final image, and describe fully the single transformation that maps T onto this final image.
[5]
(b)
E3 is an enlargement with scale factor k and centre (c, 0). E1 followed by E3 is the translation by the vector 60. Find the values of k and c.
[3]
(c)
The enlargement with centre (0, 0) and scale factor 3, followed by the enlargement with centre (a, b) and scale factor 13, is the translation by the vector 4−2. Find the values of a and b.
k = 12 (sizes must be unchanged) B1 (x, y) → (c + ½(2x − c), y) = (x + c2, y) M1 c = 12 A1
3
(c)
a = 6, b = −3
image of (x, y): (a + 13(3x − a), b + 13(3y − b)) M1 = (x + 2a3, y + 2b3) A1 2a3 = 4 and 2b3 = −2 M1 a = 6, b = −3 A1
4
Question 3Structured · 5 marks
The diagram shows shape A and shape B on a grid.
Fig. 3.1
(a)
Describe fully the single transformation that maps shape A onto shape B.
[3]
(b)
On the grid, reflect shape A in the line y = 2. Label the image C.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
Rotation, 180°, centre (−1, −1)
Rotation B1 180° B1 centre (−1, −1) B1
3
(b)
Image C drawn with vertices (1, 6), (3, 6), (1, 5)
Correct image B2 B1 for reflection in another horizontal line or correct reflection of the line y = 2 with one vertex wrong
2
Question 4Structured · 5 marksA* challenge
(a)
The point Q(5, 3) is mapped onto Q′ by a rotation of 90° anticlockwise about the origin. Q′ is then mapped onto Q″ by a reflection in the x-axis. Find the coordinates of Q″.
[2]
(b)
Describe fully the single transformation that maps any point onto its final image under these two transformations combined.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
(−3, −5)
Q′ = (−3, 5) B1 (−3, −5) B1
2
(b)
A reflection in the line y = −x
reflection B1 the line y = −x B1 full description, no extra transformations B1
3
Question 5Structured · 5 marks
The diagram shows shape A and shape B on a grid.
Fig. 5.1
(a)
Describe fully the single transformation that maps shape A onto shape B.
[3]
(b)
On the grid, reflect shape A in the line y = 0. Label the image C.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
Enlargement, scale factor 2, centre (−6, 0)
Enlargement B1 scale factor 2 B1 centre (−6, 0) B1
3
(b)
Image C drawn with vertices (−4, −1), (−2, −1), (−4, −2)
Correct image B2 B1 for reflection in another horizontal line or correct reflection of the line y = 0 with one vertex wrong
2
Question 6Structured · 5 marksA* challenge
(a)
The point Q(−1, −5) is mapped onto Q′ by a rotation of 90° anticlockwise about the origin. Q′ is then mapped onto Q″ by a reflection in the line y = x. Find the coordinates of Q″.
[2]
(b)
Describe fully the single transformation that maps any point onto its final image under these two transformations combined.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
(−1, 5)
Q′ = (5, −1) B1 (−1, 5) B1
2
(b)
A reflection in the x-axis
reflection B1 the x-axis B1 full description, no extra transformations B1
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in