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0580/11 May/Jun 2025, Question 23: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 11 (Core) · Non-calculator · 7 marks

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The question, in short

Using the given grid with triangles T, A and B, carry out a rotation of T and identify the single transformations linking T to A and to B.

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

Part (a) · 2 marks

Plot and draw the result of turning triangle T 90° clockwise about the origin (0, 0).

  1. 1Rotate 90° clockwise about (0, 0): (x, y) → (y, −x)
  2. 2(1, 1) → (1, −1), (1, 3) → (3, −1), (4, 1) → (1, −4)
  3. 3Draw the triangle at (1, −1), (3, −1), (1, −4)

AnswerCorrect rotation, points at (1, −1), (3, −1) and (1, −4)

Part (b) · 2 marks

State the one transformation, with all details, that takes triangle T to triangle A.

  1. 1(1, 1) → (−5, −3): move 6 left and 4 down
  2. 2Translation by column vector (−6, −4)

AnswerTranslation column vector (−6, −4)

Part (c) · 3 marks

State the one transformation, with all details, that takes triangle T to triangle B.

  1. 1Side lengths double (2 → 4, 3 → 6), so scale factor 2
  2. 2Centre = 2 × (1, 1) − (2, 4) = (0, −2)
  3. 3Enlargement, scale factor 2, centre (0, −2)

AnswerEnlargement, scale factor 2, centre (0, −2)

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