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0580/31 Oct/Nov 2022, Question 2: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 10 marks

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The question, in short

Using triangles A, B and C on a coordinate grid, identify transformations between them and perform a reflection and a translation on triangle A.

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

Part (ai) · 3 marks

Describe the single transformation mapping triangle A onto triangle B, giving all details.

  1. 1(3, 1) → (−3, −1), (5, 1) → (−5, −1), (3, 5) → (−3, −5): every (x, y) → (−x, −y)
  2. 2Rotation 180° about (0, 0)

AnswerRotation 180° (0, 0)

Part (aii) · 3 marks

Describe the single transformation mapping triangle A onto triangle C, giving all details.

  1. 1Sides halve: 2 → 1 and 4 → 2, so scale factor 0.5
  2. 2Lines through (3, 1) and (1, 1), and through (3, 5) and (1, 3), meet at (−1, 1)
  3. 3Enlargement, scale factor 0.5, centre (−1, 1)

AnswerEnlargement 0.5 (−1, 1)

Part (bi) · 2 marks

Reflect triangle A in the line y = 0 on the grid.

  1. 1Reflect in the x-axis: (x, y) → (x, −y)
  2. 2Draw triangle at (3, −1), (5, −1), (3, −5)

AnswerShape drawn at (3, −1), (5, −1), (3, −5)

Part (bii) · 2 marks

Translate triangle A by the vector (−7, 1) on the grid.

  1. 1Move each vertex 7 left and 1 up
  2. 2Draw triangle at (−4, 2), (−2, 2), (−4, 6)

AnswerShape drawn at (−4, 2), (−2, 2), (−4, 6)

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Also searched as: 0580/31/O/N/22 · 0580_w22_qp_31 · 0580 w22 31 · question 2.
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