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0580/32 May/Jun 2024, Question 3: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 12 marks

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The question, in short

Using four quadrilaterals A, B, C and D drawn on a 1 cm² grid, name A, find its area and perimeter, describe transformations mapping A to B, C and D, and enlarge A.

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

Part (a) · 1 mark

State the mathematical name of quadrilateral A.

  1. 1One pair of parallel sides (top and bottom): trapezium

AnswerTrapezium

Part (bi) · 1 mark

Calculate the area of quadrilateral A using the grid.

  1. 1Parallel sides 2 cm and 3 cm, height 3 cm
  2. 2Area = 1/2 × (2 + 3) × 3 = 7.5 cm²

Answer7.5

Part (bii) · 1 mark

Measure the perimeter of quadrilateral A.

  1. 1Sides: 3 cm, 2 cm, 3 cm and the slanting side √(1² + 3²) = √10 ≈ 3.16 cm
  2. 2Perimeter ≈ 3 + 2 + 3 + 3.16 = 11.2 cm

Answer11 to 11.4

Part (ci) · 2 marks

Describe fully the single transformation mapping A onto B.

  1. 1(−5, 1) → (4, −6): 9 right, 7 down
  2. 2Translation by the column vector (9, −7)

AnswerTranslation column vector (9, −7)

Part (cii) · 2 marks

Describe fully the single transformation mapping A onto C.

  1. 1(−5, 1) → (−5, −7) and (−5, 4) → (−5, −10): midpoints at y = −3
  2. 2Reflection in the line y = −3

AnswerReflection y = −3

Part (ciii) · 3 marks

Describe fully the single transformation mapping A onto D.

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

AnswerRotation (0, 0) 90° clockwise

Part (d) · 2 marks

Draw the enlargement of quadrilateral A by scale factor 2 with centre (−3, −3).

  1. 1Image = (−3, −3) + 2 × (vector from (−3, −3) to each vertex)
  2. 2(−5, 1) → (−7, 5), (−5, 4) → (−7, 11), (−3, 4) → (−3, 11), (−2, 1) → (−1, 5)
  3. 3Draw the trapezium with these vertices

AnswerTrapezium drawn at (−1, 5),(−7, 5),(−7, 11),(−3, 11)

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Also searched as: 0580/32/M/J/24 · 0580_s24_qp_32 · 0580 s24 32 · question 3.
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