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0580/32 Oct/Nov 2024, Question 9: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 7 marks

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The question, in short

Using the grid with triangles T, A and B, carry out a translation of T and identify the single transformations linking T to A and to B.

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

Part (a) · 2 marks

Move triangle T by the column vector (−5, −4) and draw the result on the grid.

  1. 1Add −5 to each x and −4 to each y
  2. 2(1, 1) → (−4, −3), (3, 3) → (−2, −1), (4, 1) → (−1, −3)
  3. 3Draw the triangle (−4, −3), (−1, −3), (−2, −1)

AnswerCorrect translation to (−4, −3), (−1, −3) and (−2, −1)

Part (b) · 2 marks

State the one transformation that takes triangle T onto triangle A, giving all details.

  1. 1Each x stays the same; only y changes: (1, 1) → (1, −3).
  2. 2So the mirror line is horizontal.
  3. 3It is halfway between y = 1 and y = −3: (1 + (−3)) ÷ 2 = −1
  4. 4Reflection, y = −1

AnswerReflection, y = −1

Part (c) · 3 marks

State the one transformation that takes triangle T onto triangle B, giving all details.

  1. 1(x, y) → (−y, x): (1, 1) → (−1, 1), (3, 3) → (−3, 3), (4, 1) → (−1, 4)
  2. 2Rotation, centre (0, 0), 90° anticlockwise

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

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Also searched as: 0580/32/O/N/24 · 0580_w24_qp_32 · 0580 w24 32 · question 9.
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