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4024/12 May/Jun 2023, Question 12: 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 two shaded shapes on a coordinate grid, identify the single transformation taking A to B, then plot A rotated 180° about the origin.

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 shape A onto shape B.

  1. 1Corresponding sides of B are twice as long as those of A, so scale factor 2
  2. 2Lines through (1, 1)→(1, 3) and (3, 1)→(5, 3) meet at (1, −1)
  3. 3Check: (1, −1) + 2 × (2, 2) = (5, 3)
  4. 4Enlargement, scale factor 2, centre (1, −1)

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

Part (b) · 2 marks

Plot the new position of shape A after turning it 180° around (0, 0).

  1. 1Rotation of 180° about (0, 0): (x, y) → (−x, −y)
  2. 2(1, 1) → (−1, −1), (1, 2) → (−1, −2), (2, 2) → (−2, −2), (3, 1) → (−3, −1)
  3. 3Plot (−1, −1), (−1, −2), (−2, −2), (−3, −1) and join them

AnswerCorrect rotation: (−1, −1), (−1, −2), (−2, −2), (−3, −1)

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Also searched as: 4024/12/M/J/23 · 4024_s23_qp_12 · 4024 s23 12 · question 12.
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