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0580/41 Oct/Nov 2024, Question 2: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 9 marks

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The question, in short

Grid with triangles A and B; carry out a reflection and an enlargement of A, describe the transformation taking A to B, and find the image of (a, b) reflected in y = k.

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

Part (ai) · 2 marks

Draw triangle A's image after reflection in the line x = 1.

  1. 1Reflect each vertex in x = 1: (1, −1) → (1, −1), (1, −3) → (1, −3), (5, −3) → (−3, −3)
  2. 2Draw the triangle with vertices (1, −1), (1, −3), (−3, −3)

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

Part (aii) · 2 marks

Draw triangle A's image after enlargement by scale factor 1/2, centre (5, 1).

  1. 1From centre (5, 1), halve each vector to a vertex: (1, −1) → (3, 0), (1, −3) → (3, −1), (5, −3) → (5, −1)
  2. 2Draw the triangle with vertices (3, −1), (5, −1), (3, 0)

AnswerTriangle at (3, −1) (5, −1) (3, 0)

Part (b) · 3 marks

Fully describe the single transformation mapping triangle A onto triangle B.

  1. 1A is turned a quarter-turn clockwise: its vertical side becomes horizontal
  2. 2(1, −1) → (−3, 5), (1, −3) → (−5, 5), (5, −3) → (−5, 1) about centre (2, 4)
  3. 3Rotation, 90° clockwise, centre (2, 4)

AnswerRotation, 90° clockwise, centre (2, 4)

Part (c) · 2 marks

For (a, b) reflected in y = k with integer k and b < k, write the image coordinates in terms of a, b, k.

  1. 1The x-coordinate is unchanged: a
  2. 2The point is k − b below the line, so the image is k − b above it: y = k + (k − b) = 2k − b
  3. 3Image = (a, 2k − b)

Answer(a, 2k − b)

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Also searched as: 0580/41/O/N/24 · 0580_w24_qp_41 · 0580 w24 41 · question 2.
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