Transformations

This lesson covers the four geometric transformations for AQA GCSE Mathematics: reflection, rotation, translation and enlargement. You need to be able to perform each transformation and, just as importantly, describe a transformation fully. Questions on transformations are very common and often carry 2-3 marks each.

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The Four Transformations

graph TD
    A[Transformations] --> B[Reflection]
    A --> C[Rotation]
    A --> D[Translation]
    A --> E[Enlargement]
    B --> B1[Mirror line]
    C --> C1[Centre, angle, direction]
    D --> D1[Column vector]
    E --> E1[Centre, scale factor]

Transformation	What Changes?	What Stays the Same?
Reflection	Orientation (flipped)	Size and shape (congruent)
Rotation	Position, orientation	Size and shape (congruent)
Translation	Position	Size, shape, orientation (congruent)
Enlargement	Size (and position)	Shape and angles (similar)

Exam Tip: Reflections, rotations, and translations all produce congruent images (same shape and size). Only enlargement changes the size of the shape, producing a similar image.

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Reflection

To perform a reflection, you need a mirror line (line of reflection).