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0580/22 Feb/Mar 2022, Question 8: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 6 marks

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The question, in short

Using the grid with triangles A and B, carry out two transformations of A and identify the single transformation linking A to B.

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

Part (ai) · 1 mark

Draw where triangle A ends up after being mirrored across the y-axis.

  1. 1Reflect in the y-axis: (x, y) → (−x, y)
  2. 2Plot (−1, 1), (−4, 2), (−3, 5) and join them

AnswerTriangle at (−1, 1) (−4, 2) (−3, 5)

Part (aii) · 2 marks

Draw triangle A shifted by the vector (−3, −4).

  1. 1Move each point 3 left and 4 down
  2. 2(1, 1) → (−2, −3), (4, 2) → (1, −2), (3, 5) → (0, 1)
  3. 3Plot and join these three points

AnswerTriangle at (−2, −3) (1, −2) (0, 1)

Part (b) · 3 marks

State completely the one transformation that takes triangle A onto triangle B.

  1. 1Sides of B are half the length of sides of A, so scale factor = 1/2
  2. 2Lines through corresponding vertices, e.g. (1, 1) to (5, 0) and (4, 2) to (6.5, 0.5), meet at (9, −1)
  3. 3Enlargement, scale factor 1/2, centre (9, −1)

AnswerEnlargement, scale factor 1/2, centre (9, −1)

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