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0580/43 Oct/Nov 2022, Question 4: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 7 marks

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The question, in short

On a grid, triangle T has vertices (1, 1), (5, 1), (1, 3) and triangle A has vertices (−4, 2), (−2, 2), (−2, 6). Carry out a reflection, an enlargement, and identify a transformation.

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

Part (a) · 2 marks

Draw the image of triangle T after reflecting it in the line y = −2.

  1. 1Each image point is the same distance on the other side of y = −2.
  2. 2(1, 1) is 3 above y = −2, so its image is 3 below: (1, −5).
  3. 3Likewise (5, 1) → (5, −5), and (1, 3) is 5 above → (1, −7).
  4. 4Triangle drawn at (1, −5), (1, −7), (5, −5)

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

Part (b) · 2 marks

Draw the image of triangle T after enlarging it by scale factor 1/2 about centre (−5, −3).

  1. 1From (−5, −3): (1, 1) is (6, 4) away → (−5, −3) + (3, 2) = (−2, −1)
  2. 2(5, 1) → (−5, −3) + (5, 2) = (0, −1)
  3. 3(1, 3) → (−5, −3) + (3, 3) = (−2, 0)
  4. 4Plot (−2, 0), (−2, −1), (0, −1) and join

AnswerTriangle drawn at (−2, 0), (−2, −1), (0, −1)

Part (c) · 3 marks

State fully the single transformation that takes triangle T onto triangle A.

  1. 1T is turned through 90° anticlockwise: (1, 1) → (−2, 2), (5, 1) → (−2, 6), (1, 3) → (−4, 2)
  2. 2Each point is the same distance from (−1, 0) before and after
  3. 3Rotation, 90° anticlockwise, centre (−1, 0)

AnswerRotation, 90° anticlockwise, centre (−1, 0)

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Also searched as: 0580/43/O/N/22 · 0580_w22_qp_43 · 0580 w22 43 · question 4.
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