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0580/33 May/Jun 2025, Question 17: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 6 marks

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The question, in short

Grid shows shapes A, B and C with given vertices; work with transformations between these shapes.

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

Part (a) · 1 mark

Sue claims one translation vector maps A to B; state why this cannot be right.

  1. 1(−2, 2) on A moves to (5, 1) on B: 7 right and 1 down
  2. 2The vector should be (7, −1): she counted 1 up instead of 1 down

AnswerShe counted 1 up instead of 1 down

Part (b) · 2 marks

Draw A turned 90° anticlockwise about the origin.

  1. 1Rotation 90° anticlockwise about (0, 0): (x, y) → (−y, x)
  2. 2(−2, 2) → (−2, −2), (−1, 2) → (−2, −1)
  3. 3(−1, 4) → (−4, −1), (−2, 5) → (−5, −2)
  4. 4Join (−4, −1), (−2, −1), (−5, −2), (−2, −2) to draw the shape

AnswerCorrect shape drawn at (−4, −1), (−2, −1), (−5, −2), (−2, −2)

Part (c) · 3 marks

Give the single transformation taking A onto C, fully described.

  1. 1Side from (−2, 2) to (−1, 2) is 1 long; image from (1, −3) to (3, −3) is 2 long, so scale factor 2
  2. 2Lines through corresponding points, e.g. (1, −3) to (−2, 2) and (3, −3) to (−1, 2), meet at (−5, 7)
  3. 3Check: (−5, 7) + 2 × (3, −5) = (1, −3)
  4. 4Enlargement, scale factor 2, centre (−5, 7)

AnswerEnlargement, scale factor 2, centre (−5, 7)

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