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Transformations: reflection, rotation, translation, enlargement

Describe and carry out the four transformations on a coordinate grid, including the details examiners expect, with worked examples.

IntermediateUpdated 5 Nov 2026
GCSEHigh School

Curriculum fit: GCSE Maths Geometry and measures (Foundation and Higher; negative scale factors are Higher). US: Geometry (Congruence).

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What is it?

A transformation changes the position or size of a shape. Translations, reflections and rotations keep the shape the same size (the image is congruent to the original). Enlargements change the size (the image is similar).

To describe a transformation fully, you must give all the details: for a rotation, for example, the angle, direction and centre.

Key formulas and ideas

  • Translation: described by a vector (x, y), where x is the move right and y is the move up.
  • Reflection: described by the mirror line, such as x = 2 or y = x.
  • Rotation: angle, direction (clockwise or anticlockwise) and centre. A 90° anticlockwise rotation about the origin maps (x, y) to (−y, x).
  • Enlargement: scale factor and centre of enlargement.

Worked examples

Example 1: Translation

Question: Translate the point (2, 3) by the vector (4, −1).

  1. Add the x movement: 2 + 4 = 6.
  2. Add the y movement: 3 − 1 = 2.

Answer: (6, 2)

Example 2: Reflection

Question: Reflect (3, 1) in the y-axis.

  1. The y-axis is the line x = 0.
  2. The x-coordinate changes sign and y stays the same.

Answer: (−3, 1)

Example 3: Rotation

Question: Rotate (2, 1) by 90° anticlockwise about the origin.

  1. Use the rule (x, y) → (−y, x).
  2. (2, 1) → (−1, 2).

Answer: (−1, 2)

Common mistakes

  • Describing a transformation with only the name, such as 'rotation', and missing the angle or centre.
  • Confusing clockwise and anticlockwise.
  • Reflecting the wrong distance from the mirror line.
  • Applying a scale factor from the wrong centre.

Practice questions

1. Translate (1, 1) by the vector (3, 2).
2. Reflect (4, 5) in the x-axis.
3. A point (1, 3) is enlarged by scale factor 2 with centre the origin. Where does it go?
4. Which transformation changes the size of a shape?
5. Rotate (3, 0) by 90° anticlockwise about the origin.

Frequently asked questions

What is the centre of enlargement?

The fixed point from which the shape is enlarged. Distances from this point are multiplied by the scale factor.

Which transformations keep the shape congruent?

Translations, reflections and rotations. Enlargements do not.

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Sources and review

Reviewed by StudyMorrow editorial review on 5 Nov 2026.