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0580/23 May/Jun 2024, Question 19: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 5 marks

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The question, in short

Using the grid showing triangles T and W, identify the single transformation taking T to W, then construct an enlargement of T with scale factor −2 about (−1, 1).

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 T onto triangle W.

  1. 1Vertical side (1, 2)−(1, 5) maps to horizontal side (4, −3)−(7, −3): a turn of 90° clockwise
  2. 2Centre (0, −2): (1, 2) → (4, −3), (1, 5) → (7, −3), (2, 5) → (7, −4)
  3. 3Rotation, 90° clockwise, centre (0, −2)

AnswerRotation, 90° clockwise, centre (0, −2)

Part (b) · 2 marks

On the grid, draw the image of triangle T after enlarging by factor −2 from centre (−1, 1).

  1. 1Image = centre − 2 × (vector from centre (−1, 1) to each vertex)
  2. 2(1, 2): vector (2, 1) → (−1 − 4, 1 − 2) = (−5, −1)
  3. 3(1, 5): vector (2, 4) → (−5, −7); (2, 5): vector (3, 4) → (−7, −7)
  4. 4Draw the triangle with vertices (−5, −1), (−5, −7) and (−7, −7)

AnswerTriangle at (−5, −1), (−5, −7), (−7, −7)

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Also searched as: 0580/23/M/J/24 · 0580_s24_qp_23 · 0580 s24 23 · question 19.
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