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0580/42 Feb/Mar 2025, Question 10: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 7 marks

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The question, in short

On a grid, triangle A has vertices (1, 3), (2, 2), (3, 5) and triangle B has vertices (−3, −1), (−1, −3), (0, −2). Carry out transformations and identify one mapping A to B.

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

Part (ai) · 2 marks

Draw the image of triangle A after reflection in the line y = 1.

  1. 1Reflect each vertex in y = 1 (same distance on the other side)
  2. 2(1, 3) → (1, −1), (2, 2) → (2, 0), (3, 5) → (3, −3)
  3. 3Draw the triangle at (2, 0), (1, −1) and (3, −3)

AnswerTriangle drawn at (2, 0), (1, −1) and (3, −3)

Part (aii) · 2 marks

Draw the image of triangle A after translation by column vector (−6, 1).

  1. 1Move each vertex 6 left and 1 up
  2. 2(1, 3) → (−5, 4), (2, 2) → (−4, 3), (3, 5) → (−3, 6)
  3. 3Draw the triangle at (−4, 3), (−5, 4) and (−3, 6)

AnswerTriangle drawn at (−4, 3), (−5, 4) and (−3, 6)

Part (b) · 3 marks

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

  1. 1(3, 5) → (−3, −1), (1, 3) → (−1, −3), (2, 2) → (0, −2)
  2. 2About (3, −1): (3, 5) is 6 up and goes to 6 left, a quarter turn anticlockwise
  3. 3Rotation, 90° anticlockwise, centre (3, −1)

AnswerRotation, 90° anticlockwise, centre (3, −1)

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Also searched as: 0580/42/F/M/25 · 0580_m25_qp_42 · 0580 m25 42 · question 10.
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