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0580/43 May/Jun 2025, Question 26: Vector Geometry

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 5 marks

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The question, in short

Quadrilateral OXPY has diagonals OP and XY crossing at T, with vectors OX = 3a, OY = 12b and YP = 5a − 2b; work out a vector and a diagonal ratio.

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

Part (a) · 1 mark

Express the vector from X to Y using a and b.

  1. 1→XY = →XO + →OY = −3a + 12b

Answer−3a + 12b

Part (b) · 4 marks

Given XT : TY = 1 : 2, determine the ratio in which T divides OP.

  1. 1→OP = →OY + →YP = 12b + 5a − 2b = 5a + 10b
  2. 2→OT = →OX + 1/3 →XY = 3a + 1/3(−3a + 12b) = 2a + 4b
  3. 3→TP = →OP − →OT = 5a + 10b − (2a + 4b) = 3a + 6b
  4. 4→OT = 2(a + 2b) and →TP = 3(a + 2b)
  5. 5OT : TP = 2 : 3

Answer2 : 3

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Also searched as: 0580/43/M/J/25 · 0580_s25_qp_43 · 0580 s25 43 · question 26.
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