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0580/31 May/Jun 2024, Question 6: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 11 marks

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The question, in short

Using a 1 cm² grid with point P and triangles A, B, C and part of D, answer reflection, trigonometry, transformation and enlargement questions.

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

Part (a) · 1 mark

Plot where P moves after being mirrored across the line y = 0.

  1. 1Reflect in the x-axis: (13, −4) → (13, 4)
  2. 2Plot P at (13, 4)

AnswerP plotted at (13,4)

Part (b) · 2 marks

Work out the size of angle a using trigonometry.

  1. 1Side opposite a = 3 (from (1, 1) to (1, 4)), side adjacent = 4 (from (1, 1) to (5, 1))
  2. 2tan a = 3/4
  3. 3a = tan⁻¹(0.75) = 36.86… ≈ 36.9°

Answer36.9 or 36.86 to 36.87

Part (ci) · 3 marks

Give the single transformation taking triangle A to triangle B, fully described.

  1. 1(x, y) → (y, −x): (1, 1) → (1, −1), (1, 4) → (4, −1), (5, 1) → (1, −5)
  2. 2Rotation, centre (0, 0), 90° clockwise

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

Part (cii) · 2 marks

Give the single transformation taking triangle A to triangle C, fully described.

  1. 1(1, 1) → (7, −4): 6 right and 5 down
  2. 2Translation by the column vector (6, −5)

AnswerTranslation column vector (6, −5)

Part (di) · 1 mark

State the enlargement scale factor that turns A into D about centre (1, 0).

  1. 1(1, 1) is 1 unit above the centre (1, 0); its image (1, 7) is 7 units above
  2. 2Scale factor = 7

Answer7

Part (dii) · 2 marks

Determine the coordinates of the remaining two corners of triangle D.

  1. 1(1, 4): 4 above centre → 28 above: (1, 28)
  2. 2(5, 1): vector (4, 1) × 7 = (28, 7) → (1 + 28, 0 + 7) = (29, 7)
  3. 3(1, 28) and (29, 7)

Answer(1,28), (29,7)

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Also searched as: 0580/31/M/J/24 · 0580_s24_qp_31 · 0580 s24 31 · question 6.
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