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4024/12 May/Jun 2021, Question 23: Describing Transformations

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Using the grid with triangles A and B, identify the single transformation taking A to B, then apply matrix P to A to draw triangle C.

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 A onto triangle B.

  1. 1A has vertices (−4, 0), (−2, 0), (−2, −4); B has vertices (2, 4), (2, 2), (−2, 2)
  2. 2Each side of A is turned a quarter-turn clockwise in B
  3. 3Centre found where perpendicular bisectors of corresponding points meet: (1, −1)
  4. 4Rotation, 90° clockwise, centre (1, −1)

AnswerRotation, 90° clockwise, (1, −1)

Part (b) · 2 marks

Use the given 2 by 2 matrix P to work out the vertices of triangle C and plot it on the grid.

  1. 1Matrix multiplies each coordinate by −1/2
  2. 2(−4, 0) → (2, 0), (−2, 0) → (1, 0), (−2, −4) → (1, 2)
  3. 3Draw triangle C with vertices (2, 0), (1, 0), (1, 2)

AnswerTriangle C at (2, 0), (1, 0), (1, 2)

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Also searched as: 4024/12/M/J/21 · 4024_s21_qp_12 · 4024 s21 12 · question 23.
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