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0580/32 May/Jun 2022, Question 9: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 7 marks

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The question, in short

Using the grid with shapes A, B and C, identify single transformations linking A to B and A to C, then draw A rotated 90° clockwise about (6, −3).

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

Part (ai) · 2 marks

Give the single transformation taking shape A exactly onto shape B.

  1. 1(2, −2) → (−5, −6): 7 left and 4 down
  2. 2Translation by column vector (−7, −4)

AnswerTranslation column vector (−7, −4)

Part (aii) · 3 marks

Give the single transformation taking shape A exactly onto shape C.

  1. 1C's sides are twice A's; lines through matching vertices, e.g. (2, −2) → (5, −4) and (4, −5) → (9, −10), meet at (−1, 0)
  2. 2Enlargement, centre (−1, 0), scale factor 2

AnswerEnlargement, centre (−1, 0), scale factor 2

Part (b) · 2 marks

Draw shape A's image after a 90° clockwise turn about (6, −3).

  1. 1Rotate 90° clockwise about (6, −3): a point (dx, dy) from the centre moves to (dy, −dx) from the centre
  2. 2(2, −2): (−4, 1) → (1, 4) gives (7, 1); (6, −2): (0, 1) → (1, 0) gives (7, −3)
  3. 3Draw the shape at (6, −3), (7, −3), (7, 1), (4, 1), (4, −1), (5, −1), (5, 0), (6, 0)

AnswerShape correctly drawn at (6, −3), (7, −3), (7, 1), (4, 1), (4, −1), (5, −1), (5, 0), (6, 0)

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Also searched as: 0580/32/M/J/22 · 0580_s22_qp_32 · 0580 s22 32 · question 9.
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