Edexcel IGCSE Maths (4MA1) · Unit 5: Geometry

IGCSE Maths Transformations Questions and Answers

Transformations questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 6 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.

6 worked examples
3 questions with mark schemes
Higher tier · calculator allowed
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Practise transformations in Unit 5 →Geometry and Trigonometry revision notes

What this topic covers

Transformations 1: Translations: Translations described by a column vector.
Transformations 2: Reflections: Reflections in horizontal / vertical / diagonal lines.
Transformations 3: Rotations (incl. combinations involving a rotation): Rotating shapes about a centre and describing rotations fully, including combinations.
Transformations 4: Enlargements (positive scale factor, finding the centre): Enlargement with a positive scale factor and finding the centre of enlargement.
Transformations 5: Harder Enlargements: Enlargements with negative and fractional scale factors.
Transformations 6: Mixed Transformations: Two-step compound transformations.

Transformations worked examples

Worked example 1: Translation

Translate \((3,\ -2)\) by the vector \(\begin{pmatrix}-5\\4\end{pmatrix}\).

Solution

Add the vector: \((3-5,\ -2+4)\).
\(=(-2,\ 2)\).

Answer: \((-2,\ 2)\)

Tip: Top number moves across, bottom number moves up.

Worked example 2: Reflection in y = −x

Reflect \((4,\ 1)\) in the line \(y=-x\).

Solution

Reflection in \(y=-x\) maps \((x,\ y)\) to \((-y,\ -x)\).
\((4,\ 1)\to(-1,\ -4)\).

Answer: \((-1,\ -4)\)

Tip: Check the midpoint (1.5, −1.5) lies on y = −x.

Worked example 3: Rotation about a point

Rotate \((2,\ 3)\) by \(90^\circ\) anticlockwise about \((1,\ 1)\).

Solution

Vector from centre: \((1,\ 2)\).
Rotating 90° anticlockwise: \((a,b)\to(-b,a)\), giving \((-2,\ 1)\).
Add back to the centre: \((-1,\ 2)\).

Answer: \((-1,\ 2)\)

Tip: Tracing paper is a good check.

Worked example 4: Enlargement from a centre

Enlarge \((5,\ 2)\) by scale factor 3, centre \((2,\ 1)\).

Solution

Vector from centre: \((3,\ 1)\).
Multiply by 3: \((9,\ 3)\).
Image: \((2+9,\ 1+3)=(11,\ 4)\).

Answer: \((11,\ 4)\)

Tip: Always measure from the centre of enlargement.

Worked example 5: Negative fractional enlargement

Enlarge \((4,\ -6)\) by scale factor \(-\tfrac{1}{2}\), centre \((0,\ 0)\).

Solution

Multiply the coordinates by \(-\tfrac{1}{2}\).
\((-2,\ 3)\).

Answer: \((-2,\ 3)\)

Tip: A negative scale factor puts the image on the other side of the centre.

Worked example 6: Combining transformations

Reflect \((2,\ 5)\) in the x-axis, then rotate the image \(180^\circ\) about the origin. What single transformation has the same effect?

Solution

Reflect: \((2,\ -5)\).
Rotate 180°: \((-2,\ 5)\).
\((2,5)\to(-2,5)\): reflection in the y-axis.

Answer: Reflection in the y-axis

Tip: Test with a general point (x, y) to be sure.

Transformations exam-style questions

Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 2 marks

Triangle A has vertices (1, 1), (4, 1) and (1, 3). Triangle A is rotated 180° about the origin. Write down the coordinates of the vertices of the image.

Show the answer and mark scheme

B2 (−1, −1), (−4, −1), (−1, −3) (B1 for 2 correct vertices or a correct rotation about a different centre)

Answer: (−1, −1), (−4, −1), (−1, −3)

Question 2 · medium · 3 marks

Triangle A has vertices (1, 2), (3, 2) and (3, 5). Triangle B has vertices (−2, 1), (−2, 3) and (−5, 3). Describe fully the single transformation that maps triangle A onto triangle B.

Show the answer and mark scheme

B1 rotation
B1 90° anticlockwise (or 270° clockwise)
B1 centre (0, 0)

Answer: Rotation 90° anticlockwise about (0, 0)

Question 3 · hard · 2 marks

The point A(5, 3) is rotated 90° clockwise about the point (2, −1). Find the coordinates of the image of A.

Show the answer and mark scheme

M1 vector from centre (3, 4) rotated to (4, −3)
A1 (6, −4)

Answer: (6, −4)

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise transformations for the exam

Unit 5 practice: Geometry in the student hub (more questions with mark schemes)
IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
IGCSE Maths 4MA1 examiner report summary: where students lose marks

Questions students ask

Which Edexcel IGCSE Maths papers test transformations?

Either Higher tier paper, 1H or 2H, can test transformations: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more transformations questions?

In the IGCSE student hub: Unit 5 (Geometry) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

IGCSE Maths Transformations Questions and Answers

What this topic covers

Transformations worked examples

Worked example 1: Translation

Solution

Worked example 2: Reflection in y = −x

Solution

Worked example 3: Rotation about a point

Solution

Worked example 4: Enlargement from a centre

Solution

Worked example 5: Negative fractional enlargement

Solution

Worked example 6: Combining transformations

Solution

Transformations exam-style questions

Question 1 · easy · 2 marks

Question 2 · medium · 3 marks

Question 3 · hard · 2 marks

Revise transformations for the exam

Questions students ask

More Unit 5 topics: Geometry