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0580/43 Oct/Nov 2023, Question 3: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 9 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 construct three images of A under a reflection, a translation and an enlargement.

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. 1Corresponding sides turn through 90° anticlockwise, and the triangle keeps its size, so it is a rotation
  2. 2Centre (2, 7): e.g. (−4, 3) is 6 left, 4 down from (2, 7) and maps to (6, 1), 4 right, 6 down
  3. 3Rotation, 90° anticlockwise, centre (2, 7)

AnswerRotation, 90° anticlockwise, (2, 7)

Part (bi) · 2 marks

Plot the image of triangle A after reflecting it in the horizontal line y = 1.

  1. 1Reflect in y = 1: (x, y) → (x, 2 − y)
  2. 2(−4, 3) → (−4, −1), (−3, 3) → (−3, −1), (−4, 6) → (−4, −4)

AnswerImage at (−4, −1), (−3, −1), (−4, −4)

Part (bii) · 2 marks

Plot the image of triangle A after shifting it by the vector (5, −7).

  1. 1Move each vertex 5 right and 7 down
  2. 2(−4, 3) → (1, −4), (−3, 3) → (2, −4), (−4, 6) → (1, −1)

AnswerImage at (2, −4), (1, −4), (1, −1)

Part (biii) · 2 marks

Plot the image of triangle A after enlarging it by scale factor 2 about the point (−4, 5).

  1. 1Double each vertex's distance from (−4, 5)
  2. 2(−4, 3) is 2 below the centre → (−4, 1)
  3. 3(−3, 3) is 1 right, 2 below → (−2, 1)
  4. 4(−4, 6) is 1 above → (−4, 7)

AnswerImage at (−4, 7), (−4, 1), (−2, 1)

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Also searched as: 0580/43/O/N/23 · 0580_w23_qp_43 · 0580 w23 43 · question 3.
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