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0580/31 Oct/Nov 2024, Question 4: Constructing Triangles

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 6 marks

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The question, in short

Using ruler and compasses only, construct the missing triangle to finish parallelogram ABCD with sides 8 cm and 6 cm, keeping your arcs; then work with shapes A and B on the grid.

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

Part (a) · 2 marks

With AB and BC already drawn, construct triangle ACD so ABCD becomes a parallelogram; show all compass arcs and use no other tools.

  1. 1The missing sides are CD = 6 cm (= AB) and AD = 8 cm (= BC)
  2. 2Compasses set to 6 cm, centre C: draw an arc
  3. 3Compasses set to 8 cm, centre A: draw an arc crossing the first; the crossing is D
  4. 4Join CD and AD with a ruler, leaving the arcs

AnswerCorrect parallelogram

Part (bi) · 2 marks

Give the single transformation, fully described, that takes shape A onto shape B on the grid.

  1. 1(1, 1) → (−5, 3): x changes by −6, y changes by +2
  2. 2Translation by column vector (−6, 2)

AnswerTranslation, column vector (−6, 2)

Part (bii) · 2 marks

Draw shape A's image on the grid after turning it 90° anticlockwise about the point (5, 1).

  1. 1Centre (5, 1) stays fixed; each point (5 + a, 1 + b) goes to (5 − b, 1 + a)
  2. 2(1, 1) → (5, −3), (1, 4) → (2, −3), (3, 4) → (2, −1), (3, 2) → (4, −1), (5, 2) → (4, 1)
  3. 3Draw the shape (5, 1) (5, −3) (2, −3) (2, −1) (4, −1) (4, 1)

AnswerCorrect shape with coordinates (5, 1) (5, −3) (2, −3) (2, −1) (4, −1) (4, 1)

Stuck on a step? Read the free lesson: Constructing Triangles

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Also searched as: 0580/31/O/N/24 · 0580_w24_qp_31 · 0580 w24 31 · question 4.
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