Transformations - AQA GCSE Mathematics Revision

Topic overview

What you need to know

Transformations is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A transformation that moves every point of a shape the same distance in the same direction. Described by a column vector. Used to describe a translation: the top number is horizontal movement, the bottom is vertical. E.g. (3, −2) means 3 right, 2 down. A transformation that turns a shape around a fixed centre point by a given angle and direction.

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

Translation: A transformation that moves every point of a shape the same distance in the same direction. Described by a column vector.
Column Vector: Used to describe a translation: the top number is horizontal movement, the bottom is vertical. E.g. (3, −2) means 3 right, 2 down.
Rotation: A transformation that turns a shape around a fixed centre point by a given angle and direction.
Reflection: A transformation that produces a mirror image of a shape across a line of reflection.

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

Enlargement: A transformation that changes the size of a shape by a scale factor from a centre of enlargement.
Scale Factor (Enlargement): The multiplier for each length. SF > 1 makes it bigger, 0 < SF < 1 makes it smaller, negative SF inverts it.
Congruent: Shapes that are exactly the same size and shape. Translations, rotations, and reflections produce congruent shapes.
Similar: Shapes that have the same angles but different sizes. Enlargements produce similar shapes.

Core knowledge

Key facts for Transformations

8 essentials

Translation

A transformation that moves every point of a shape the same distance in the same direction. Described by a column vector.

Column Vector

Used to describe a translation: the top number is horizontal movement, the bottom is vertical. E.g. (3, −2) means 3 right, 2 down.

Rotation

A transformation that turns a shape around a fixed centre point by a given angle and direction.

Reflection

A transformation that produces a mirror image of a shape across a line of reflection.

Enlargement

A transformation that changes the size of a shape by a scale factor from a centre of enlargement.

Scale Factor (Enlargement)

The multiplier for each length. SF > 1 makes it bigger, 0 < SF < 1 makes it smaller, negative SF inverts it.

Congruent

Shapes that are exactly the same size and shape. Translations, rotations, and reflections produce congruent shapes.

Similar

Shapes that have the same angles but different sizes. Enlargements produce similar shapes.

Active recall

Close the notes and answer these

1.Without looking, explain translation and give one example or consequence.
2.Without looking, explain column vector and give one example or consequence.
3.Without looking, explain rotation and give one example or consequence.
4.Without looking, explain reflection and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

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