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0580/22 May/Jun 2023, Question 10: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 6 marks

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The question, in short

Using the grid with shapes A and B, identify the single transformation linking A to B, then perform a 90° clockwise rotation and an enlargement by −2 on shape A.

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

Part (a) · 2 marks

State the one transformation that takes shape A onto shape B, giving all its details.

  1. 1Shape B is a mirror image of A, so it is a reflection.
  2. 2(3, 1) maps to (3, 3): the mirror is halfway, at y = 2.
  3. 3Check: (6, −3) and (6, 7) are both 5 units from y = 2.
  4. 4Reflection in the line y = 2

AnswerReflection, y = 2

Part (b) · 2 marks

Draw shape A after turning it 90° clockwise around (−1, 2).

  1. 1About (−1, 2), 90° clockwise: (x, y) → (y − 3, 1 − x)
  2. 2(3, 1) → (−2, −2), (3, −1) → (−4, −2)
  3. 3(4, −3) → (−6, −3), (6, −3) → (−6, −5)
  4. 4Draw the shape with vertices (−2, −2), (−4, −2), (−6, −3), (−6, −5)

AnswerShape at (−2, −2), (−6, −5), (−6, −3), (−4, −2)

Part (c) · 2 marks

Draw shape A after enlarging it by scale factor −2 from centre (2, 0).

  1. 1From centre (2, 0), multiply each displacement by −2: (x, y) → (6 − 2x, −2y)
  2. 2(3, 1) → (0, −2), (3, −1) → (0, 2)
  3. 3(4, −3) → (−2, 6), (6, −3) → (−6, 6)
  4. 4Draw the shape with vertices (0, −2), (0, 2), (−2, 6), (−6, 6)

AnswerShape at (0, −2), (0, 2), (−2, 6), (−6, 6)

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Also searched as: 0580/22/M/J/23 · 0580_s23_qp_22 · 0580 s23 22 · question 10.
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