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4024/12 Oct/Nov 2024, Question 16: Describing Transformations

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

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The question, in short

On a grid, shape A and shape B are given by their vertices; carry out a translation of A and identify the single transformation taking A to B.

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

Part (a) · 2 marks

Move shape A by the vector 3 right and 5 down, and draw the resulting shape on the grid.

  1. 1Translation (3, −5): add 3 to each x-coordinate and subtract 5 from each y-coordinate
  2. 2(−2, 2) → (1, −3), (2, 2) → (5, −3), (2, 3) → (5, −2)
  3. 3(−1, 3) → (2, −2), (−1, 4) → (2, −1), (−2, 4) → (1, −1)
  4. 4Join (1, −1), (2, −1), (2, −2), (5, −2), (5, −3), (1, −3)

AnswerCorrect shape drawn with coordinates (1, −1), (2, −1), (2, −2), (5, −2), (5, −3), (1, −3)

Part (b) · 3 marks

State the one transformation, with all its details, that maps shape A exactly onto shape B.

  1. 1Shape B is the same size as A but turned through a quarter turn, so it is a rotation
  2. 2(2, 2) → (5, 3) and (−2, 4) → (7, 7) under a 90° clockwise turn about (4, 1)
  3. 3Rotation, 90° clockwise, centre (4, 1)

AnswerRotation, 90° clockwise, centre (4, 1)

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Also searched as: 4024/12/O/N/24 · 4024_w24_qp_12 · 4024 w24 12 · question 16.
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