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0580/32 Oct/Nov 2021, Question 9: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 8 marks

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The question, in short

Using triangles T, A and B on a grid, describe transformations mapping T to A and T to B, then draw T's image after a given translation.

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

Part (a) · 3 marks

Describe fully the single transformation taking triangle T onto triangle A.

  1. 1Lengths double (2 → 4, 3 → 6), so scale factor 2
  2. 2Lines through corresponding vertices, e.g. (1, 1) → (3, 3) and (4, 1) → (9, 3), meet at (−1, −1)
  3. 3Enlargement, centre (−1, −1), scale factor 2

AnswerEnlargement, centre (−1, −1), scale factor 2

Part (b) · 3 marks

Describe fully the single transformation taking triangle T onto triangle B.

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

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

Part (c) · 2 marks

Draw on the grid the image of triangle T after translation by column vector (5, −3).

  1. 1Add 5 to x and subtract 3 from y: (1, 1) → (6, −2), (1, 3) → (6, 0), (4, 1) → (9, −2)
  2. 2Draw the triangle (6, 0), (6, −2), (9, −2)

AnswerTriangle at (6, 0), (6, −2), (9, −2)

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Also searched as: 0580/32/O/N/21 · 0580_w21_qp_32 · 0580 w21 32 · question 9.
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