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0580/32 Feb/Mar 2025, Question 20: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 9 marks

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The question, in short

Using three triangles A, B and C drawn on a 1 cm² coordinate grid, carry out a rotation, identify two transformations and find an angle in triangle C.

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

Part (a) · 2 marks

Draw the result of turning shape A 90° clockwise about the point (0, 3) on the grid.

  1. 1Centre (0, 3) stays fixed
  2. 2(2, 3) is 2 right of the centre, rotates to 2 below: (0, 1)
  3. 3(2, 4) is 2 right and 1 up, rotates to 1 right and 2 down: (1, 1)
  4. 4Draw the triangle with vertices (0, 1), (0, 3), (1, 1)

AnswerTriangle with vertices (0, 1), (0, 3), (1, 1)

Part (bi) · 2 marks

State the single transformation that takes triangle A to triangle B, giving all details.

  1. 1(0, 3) → (2, 2): 2 right and 1 down
  2. 2Translation by column vector (2, −1)

AnswerTranslation by column vector (2, −1)

Part (bii) · 3 marks

State the single transformation that takes triangle A to triangle C, giving all details.

  1. 1C's sides are twice A's (base 4 not 2, height 2 not 1), and C is the same way up
  2. 2Lines through corresponding vertices, e.g. (−5, 3)→(0, 3) and (−1, 5)→(2, 4), meet at (5, 3)
  3. 3Enlargement, centre (5, 3), scale factor 2

AnswerEnlargement, centre (5, 3), scale factor 2

Part (c) · 2 marks

Work out the smallest angle inside triangle C.

  1. 1Triangle C has horizontal side 4 and vertical side 2
  2. 2The smallest angle is opposite the shortest side: tan x = 2/4
  3. 3x = tan⁻¹(0.5) = 26.56…° ≈ 26.6°

Answer26.6 or 26.56 to 26.57

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Also searched as: 0580/32/F/M/25 · 0580_m25_qp_32 · 0580 m25 32 · question 20.
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