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0580/23 May/Jun 2025, Question 5: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 7 marks

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The question, in short

Using the grid with triangles A and B, identify the single transformation taking A to B, then draw two images of A.

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

Part (a) · 3 marks

State the one transformation, with all its details, that carries triangle A onto triangle B.

  1. 1Side from (1, 3) to (4, 1) becomes (1, 5) to (10, −1): lengths × 3, same orientation
  2. 2Scale factor 3
  3. 3Join corresponding vertices, e.g. (1, 3) to (1, 5) and (4, 1) to (10, −1); the lines meet at (1, 2)
  4. 4Enlargement, scale factor 3, centre (1, 2)

AnswerEnlargement, scale factor 3, centre (1, 2)

Part (bi) · 2 marks

Draw where triangle A lands after being reflected in the vertical line x = −1.

  1. 1Each point moves to the same distance on the other side of x = −1: x → −2 − x
  2. 2(1, 3) → (−3, 3), (2, 4) → (−4, 4), (4, 1) → (−6, 1)
  3. 3Plot and join these points

AnswerTriangle at (−6, 1), (−3, 3), (−4, 4)

Part (bii) · 2 marks

Draw triangle A after turning it 90° clockwise about the point (1, −2).

  1. 1Relative to (1, −2): (1, 3) is (0, 5), (2, 4) is (1, 6), (4, 1) is (3, 3)
  2. 290° clockwise: (a, b) → (b, −a), giving (5, 0), (6, −1), (3, −3)
  3. 3Add back (1, −2): (6, −2), (7, −3), (4, −5)
  4. 4Plot and join these points

AnswerTriangle at (4, −5), (6, −2), (7, −3)

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Also searched as: 0580/23/M/J/25 · 0580_s25_qp_23 · 0580 s25 23 · question 5.
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