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Geometry & Measures · Foundation & Higher

Transformations (RREST)

The four transformations are Rotation, Reflection, Enlargement and Translation (RREST). Each moves or resizes a shape in a specific way, and you must describe them fully.

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Key facts to remember

  • 1Translation: described by a column vector (x, y) — x is right/left, y is up/down.
  • 2Reflection: described by the mirror line (e.g. y = x, x = 2).
  • 3Rotation: described by the centre, angle, and direction (clockwise/anticlockwise).
  • 4Enlargement: described by the centre of enlargement and scale factor. Scale factor > 1 enlarges, 0 < SF < 1 reduces.
  • 5After a translation, reflection or rotation, the shape is congruent to the original (same size and shape).
  • 6Enlargement changes size but preserves angles.
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Worked examples

Example 1

Describe fully the transformation that maps shape A to shape B, where B is the mirror image of A in the line y = −1.

Working

  1. The shapes are congruent and mirror images → reflection
  2. Identify the mirror line between corresponding points → y = −1
  3. Transformation: Reflection in the line y = −1
AnswerReflection in the line y = −1
Example 2

Enlarge triangle with vertices (1,1), (3,1), (1,3) by scale factor 2, centre (0,0).

Working

  1. Multiply each coordinate by the scale factor 2
  2. (1,1) → (2,2)
  3. (3,1) → (6,2)
  4. (1,3) → (2,6)
AnswerNew vertices: (2,2), (6,2), (2,6)
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Common mistakes

✗Not fully describing a transformation — missing the mirror line, centre of rotation, or scale factor.
✗Using scale factor incorrectly in enlargement: multiplying coordinates by SF from the wrong origin.
✗Confusing rotation direction (clockwise vs anticlockwise).
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Exam tips

✓Always give a full description: rotation needs centre + angle + direction; enlargement needs centre + scale factor.
✓Tracing paper is very helpful for rotations — ask for it in exams if not provided.

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