GCSE MATHS PRACTICE

GCSE Transformations Questions

A reflection flips a shape in a mirror line. A translation moves every point by the same vector. A rotation needs a centre, angle and direction. An enlargement needs a centre and scale factor. Here each question starts from a separate triangle: write the coordinates of its image vertices. All enlargement scale factors on this page are positive.

Updated 12 October 2026

Worked example

Reflect A(1, 1), B(3, 1), C(1, 3) in the y-axis.

Each grid square is 1 unit. Solid: original. Dashed: reflected image.

Reflection in the y-axis maps (x, y) to (−x, y). Each point stays the same distance from the mirror line.
Change each x-coordinate to its opposite and leave each y-coordinate unchanged.
The image vertices are A′(−1, 1), B′(−3, 1), C′(−1, 3). The dashed triangle shows the image.

Answer: A′(−1, 1), B′(−3, 1), C′(−1, 3)

Practice questions

1
Reflect A(1, 1), B(3, 1), C(1, 3) in the x-axis. Give A′, B′ and C′.
Each grid square is 1 unit. Only the original shape is shown.
Enlarged diagram
100%Scroll to inspect when enlarged.
2
Translate A(−3, −1), B(−1, −1), C(−3, 1) by the column vector (42). Give A′, B′ and C′.
Each grid square is 1 unit. Only the original shape is shown.
Enlarged diagram
100%Scroll to inspect when enlarged.
3
Rotate A(1, 1), B(3, 1), C(1, 2) through 90° anticlockwise about O(0, 0). Give A′, B′ and C′.
Each grid square is 1 unit. Only the original shape is shown.
Enlarged diagram
100%Scroll to inspect when enlarged.
4
Enlarge A(1, 1), B(2, 1), C(1, 2) by scale factor 2 with centre O(0, 0). Give A′, B′ and C′.
Each grid square is 1 unit. Only the original shape is shown.
Enlarged diagram
100%Scroll to inspect when enlarged.

Show answers

1. A′(1, −1), B′(3, −1), C′(1, −3)
2. A′(1, 1), B′(3, 1), C′(1, 3)
3. A′(−1, 1), B′(−1, 3), C′(−2, 1)
4. A′(2, 2), B′(4, 2), C′(2, 4)

Common mistakes

Swapping vector entries — The top entry is horizontal movement; the bottom entry is vertical.
Rotating about the wrong point — Use the stated centre and direction.
Enlarging by adding — Multiply each displacement from the centre by the scale factor.

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GCSE Transformations Questions

Updated 12 October 2026

Worked example

Reflect A(1, 1), B(3, 1), C(1, 3) in the y-axis.

Each grid square is 1 unit. Solid: original. Dashed: reflected image.

Reflection in the y-axis maps (x, y) to (−x, y). Each point stays the same distance from the mirror line.

Change each x-coordinate to its opposite and leave each y-coordinate unchanged.

The image vertices are A′(−1, 1), B′(−3, 1), C′(−1, 3). The dashed triangle shows the image.

Answer: A′(−1, 1), B′(−3, 1), C′(−1, 3)

Practice questions

Reflect A(1, 1), B(3, 1), C(1, 3) in the x-axis. Give A′, B′ and C′.

Each grid square is 1 unit. Only the original shape is shown.

Translate A(−3, −1), B(−1, −1), C(−3, 1) by the column vector (42). Give A′, B′ and C′.

Each grid square is 1 unit. Only the original shape is shown.

Rotate A(1, 1), B(3, 1), C(1, 2) through 90° anticlockwise about O(0, 0). Give A′, B′ and C′.

Each grid square is 1 unit. Only the original shape is shown.

Enlarge A(1, 1), B(2, 1), C(1, 2) by scale factor 2 with centre O(0, 0). Give A′, B′ and C′.

Each grid square is 1 unit. Only the original shape is shown.

Show answers

1. A′(1, −1), B′(3, −1), C′(1, −3)
2. A′(1, 1), B′(3, 1), C′(1, 3)
3. A′(−1, 1), B′(−1, 3), C′(−2, 1)
4. A′(2, 2), B′(4, 2), C′(2, 4)

GCSE Transformations Questions

Worked example

Practice questions

Common mistakes

Related resources

More Maths Unlocked lessons

GCSE Transformations Questions

Worked example

Practice questions

Common mistakes

Related resources

More Maths Unlocked lessons