The four transformations are: reflection, rotation, translation and enlargement. At Higher tier you must describe them fully, apply them, and work with negative scale factors for enlargements. Combined transformations may also be examined.
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Revising transformations the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Transformations GCSE” on the site for the complete guide.
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Key facts to remember
1Reflection: needs the mirror line equation (e.g. y = x, x = 2).
2Rotation: needs the centre of rotation, angle, and direction (clockwise or anticlockwise).
3Translation: described by a column vector (x/y) — positive x moves right, positive y moves up.
4Enlargement: needs the centre of enlargement and scale factor. Scale factor = image length ÷ original length.
5Negative scale factor: the image is on the opposite side of the centre and inverted.
6Transformations that preserve shape and size (isometries): reflection, rotation, translation.
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Worked examples
Example 1
Describe fully the single transformation that maps triangle A onto triangle B, where A has vertices (1,1),(3,1),(3,4) and B has vertices (−1,1),(−3,1),(−3,4).
Working
Compare the x-coordinates: each x has been negated (1→−1, 3→−3). y-values unchanged.
This is a reflection in the y-axis (the line x = 0).
Check: reflecting (1,1) in x = 0 gives (−1,1) ✓
AnswerReflection in the y-axis (x = 0).
Example 2
Enlarge triangle T with vertices (2,1),(4,1),(4,3) by scale factor −2 about centre (1,1).
Working
Find vector from centre to each vertex, multiply by −2.