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0580/32 Oct/Nov 2023, Question 9: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 10 marks

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The question, in short

Using triangles A, B and C on a coordinate grid, identify transformations between them and draw two transformed images of triangle A.

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

Part (a) · 3 marks

Describe fully the single transformation mapping triangle A onto triangle B.

  1. 1(x, y) → (y, −x): (−4, 1) → (1, 4), (−4, −1) → (−1, 4), (−1, 1) → (1, 1)
  2. 2Rotation, centre (0, 0), 90° clockwise

AnswerRotation, centre (0, 0), 90° clockwise

Part (b) · 3 marks

Describe fully the single transformation mapping triangle A onto triangle C.

  1. 1Sides ×1.5 (2 → 3, 3 → 4.5): scale factor 1.5
  2. 2Centre = (1.5 × (−4, 1) − (−5.5, 5)) ÷ 0.5 = (−1, −7)
  3. 3Enlargement, scale factor 1.5, centre (−1, −7)

AnswerEnlargement, scale factor 1.5, centre (−1, −7)

Part (c) · 2 marks

Translate triangle A by the column vector (6, −4) on the grid.

  1. 1Add 6 to each x and −4 to each y
  2. 2(−4, 1) → (2, −3), (−4, −1) → (2, −5), (−1, 1) → (5, −3)

AnswerCorrect translation: vertices (2, −3), (2, −5), (5, −3)

Part (d) · 2 marks

Reflect triangle A in the line y = −2 on the grid.

  1. 1Each y becomes −4 − y (same distance from y = −2 on the other side)
  2. 2(−4, 1) → (−4, −5), (−4, −1) → (−4, −3), (−1, 1) → (−1, −5)

AnswerCorrect reflection: vertices (−4, −3), (−4, −5), (−1, −5)

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Also searched as: 0580/32/O/N/23 · 0580_w23_qp_32 · 0580 w23 32 · question 9.
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