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0580/42 May/Jun 2021, Question 7: Translation

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks

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The question, in short

Grid with triangles T and A; perform three transformations on T and identify the single transformation mapping T to A.

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

Part (ai) · 2 marks

Draw T's image after translation by column vector (2, −1).

  1. 1Move each vertex 2 right, 1 down: (2, 1) → (4, 0), (2, 4) → (4, 3), (4, 4) → (6, 3)
  2. 2Draw the triangle with these vertices

AnswerTriangle at (4, 0) (4, 3) (6, 3)

Part (aii) · 2 marks

Draw T's image after a 90° clockwise rotation about the origin.

  1. 190° clockwise about O: (x, y) → (y, −x)
  2. 2(2, 1) → (1, −2), (2, 4) → (4, −2), (4, 4) → (4, −4)
  3. 3Draw the triangle with these vertices

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

Part (aiii) · 2 marks

Draw T's image after enlargement, scale factor −1/2, centre (−2, 3).

  1. 1Image = centre − 1/2 × (point − centre), centre (−2, 3)
  2. 2(2, 1): −2 − 2 = −4, 3 + 1 = 4 → (−4, 4)
  3. 3(2, 4) → (−4, 2.5), (4, 4) → (−5, 2.5)
  4. 4Draw the triangle with these vertices

AnswerTriangle at (−4, 4), (−4, 2.5), (−5, 2.5)

Part (b) · 2 marks

Describe fully the single transformation that maps T onto A.

  1. 1(x, y) → (−y, −x): (2, 1) → (−1, −2), (2, 4) → (−4, −2), (4, 4) → (−4, −4)
  2. 2Reflection in y = −x

AnswerReflection in y = −x

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Also searched as: 0580/42/M/J/21 · 0580_s21_qp_42 · 0580 s21 42 · question 7.
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