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4024/12 May/Jun 2025, Question 12: Describing Transformations

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 8 marks

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The question, in short

Grid shows triangles A and B with given vertices. Describe the single transformation mapping A to B, reflect A in x = −1, and work with an enlargement of A about (0, 0).

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 3 marks

Describe fully the one transformation taking triangle A onto triangle B.

  1. 1B is A turned a quarter-turn clockwise
  2. 2(1, 1) → (−2, −2), (4, 1) → (−2, −5), (3, 2) → (−1, −4) fit centre (−2, 1)
  3. 3Rotation, 90° clockwise, centre (−2, 1)

AnswerRotation, 90° clockwise, centre (−2, 1)

Part (b) · 2 marks

Draw triangle A's image after reflection in the line x = −1.

  1. 1Reflect in x = −1: x → −2 − x
  2. 2(1, 1) → (−3, 1), (4, 1) → (−6, 1), (3, 2) → (−5, 2)

AnswerTriangle at (−6, 1), (−3, 1), (−5, 2)

Part (ci) · 1 mark

Given one vertex of triangle C is (12, 3), find the enlargement scale factor k.

  1. 1(4, 1) → (12, 3), so k = 12 ÷ 4 = 3

Answer3

Part (cii) · 2 marks

Find the coordinates of the remaining two vertices of triangle C.

  1. 1(12, 3) comes from (4, 1): 4 × 3 = 12 and 1 × 3 = 3
  2. 2So k = 3: multiply every coordinate by 3.
  3. 3(1, 1) → (3, 3) and (3, 2) → (9, 6)
  4. 4Other two vertices: (3, 3) (9, 6)

Answer(3, 3) (9, 6)

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