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Combined transformations

Free Printable Combined transformations PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 6)

Download free combined transformations worksheets (PDF), GCSE maths past paper questions and worked solutions for Combined transformations (6N). This is a Grade 6 geometry topic from the GCSE questions by topic collection for Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our combined transformations revision notes and worked examples with diagrams, try real GCSE past paper combined transformations questions with step-by-step solutions, or download a PDF of all combined transformations worksheet links.

Free Combined transformations PDF Worksheets & Answers

Grade 6 • Topic 6N
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
GCSE topic booklet & answers
 Qs Ans
PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
PMT (AQA)
AQA GCSE topic questions & solutions
 Qs Ans
PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Grade 6 topics
6A - Recurring decimals6B - Harder indices
6C - The product rule6D - Repeated change
6E - Triple brackets6F - Parallel and perpendicular
6G - Inequalities on graphs6H - Similar shapes (area and vol)
6J - Negative scale factors6K - Circle theorems
6L - Cumulative frequency6M - Box plots
6N - Combined transformations6P - Capture recapture
GCSE Maths Grade 6 Revision Notes & Method

Guide to Combined transformations: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

For combined transformations, apply the first transformation to the original shape to draw an intermediate image, then apply the second transformation to that intermediate image.

When asked to describe the single transformation that maps the starting shape directly onto the final shape, check whether the orientation has flipped (reflection) or stayed the same (rotation/translation). Two reflections in perpendicular axes (such as the x-axis and y-axis) are equivalent to a rotation of 180° about their intersection.

Example 1: Shape A has corner (2, 3). It is reflected in the x-axis to give B, then B is reflected in the y-axis to give C. Describe the single transformation from A to C.

A(2,3) B(2,−3) C(−2,−3)

Solution:

(2, 3) → B(2, −3) → C(−2, −3), so (x, y) → (−x, −y)
Answer: Rotation of 180° about (0, 0)

Example 2: Shape P is translated by vector (4, −1) to give Q, then Q is translated by (−6, 5) to give R. Describe the single transformation from P to R.

Solution:

Add the two translation vectors together:
Horizontal: 4 + (−6) = −2
Vertical: −1 + 5 = 4
Answer: Translation by column vector (−2, 4)
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Combined transformations Questions & Answers

Past Paper Example 1 GCSE Nov 2020 3H Q11 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows a triangle **P** on a grid.
xyP–7–6–5–4–3–2–11234567–7–6–5–4–3–2–1123456O
(a) Describe fully the single transformation that maps triangle **P** onto triangle **R**. [3 marks]
(b) Write down the coordinates of point A. [1 mark]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
P vertices: (1,2), (1,5), (2,5) → Q: (–1,–2), (–1,–5), (–2,–5) → R: (4,–4), (4,–7), (3,–7) M2 C1
Answer (a): Rotation of 180° about (2.5, –1)
Part (b) Solution:
Midpoint of (1,2) and (4,–4) is (2.5, –1). B1
Answer (b): (2.5, –1)
Past Paper Example 2 GCSE May 2024 1H Q11 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
xyA–6–5–4–3–2–1123456–6–5–4–3–2–1123456O
Triangle A is translated by the vector (6-4) to give triangle B.
Triangle B is rotated 90° clockwise about the point (1, 2) to give triangle C.
Describe fully the single transformation that maps triangle A onto triangle C.
Triangle A is translated by the vector (6-4) to give triangle B.
Triangle B is rotated 90° clockwise about the point (1, 2) to give triangle C.
Describe fully the single transformation that maps triangle A onto triangle C.
Worked Solution & Mark Scheme (3 marks)
A has vertices (–3, 2), (–2, 2), (–2, 4) M1
B has vertices (3, –2), (4, –2), (4, 0) M1
Rotating B 90° clockwise about (1, 2) gives C at (–3, 0), (–3, –1), (–1, –1)
Single transformation from A to C is a rotation 90° clockwise about centre (–4, 1). C1
xyABC–6–5–4–3–2–1123456–6–5–4–3–2–1123456O
Answer: Rotation, 90° clockwise, centre (-4, 1)
Past Paper Example 3 GCSE Nov 2019 2H Q24 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
xy–6–5–4–3–2–1123456–6–5–4–3–2–1123456OABCD
Square ABCD is transformed by a combined transformation of a reflection in the line x = -1 followed by a rotation.
Under the combined transformation, two vertices of the square ABCD are invariant.
Describe fully one possible rotation.
Square ABCD is transformed by a combined transformation of a reflection in the line x = -1 followed by a rotation.
Under the combined transformation, two vertices of the square ABCD are invariant.
Describe fully one possible rotation.
Worked Solution & Mark Scheme (2 marks)
Reflecting ABCD in x = –1 gives A'(–3, 4), B'(–5, 4), C'(–5, 2), D'(–3, 2) M1
Rotating 90° clockwise about (–1, 0) maps B'(–5, 4) → B(3, 4) and D'(–3, 2) → D(1, 2), leaving B and D invariant. C1
Answer: Rotation 90° clockwise about (–1, 0) [or 90° anticlockwise about (–1, 6), or 180° about (–1, 2), or 180° about (–1, 4)]

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