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0580/42 Oct/Nov 2025, Question 18: Vector Geometry

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 4 marks

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The question, in short

Quadrilateral OABC has OA parallel to CB with OA:CB = 4:3, vectors OA = a and OB = b. Find vector AB, then vector AM where M is the midpoint of OC.

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

Part (a) · 1 mark

Find the vector AB in terms of a and b.

  1. 1→AB = →AO + →OB = −a + b = b − a

Answerb − a

Part (b) · 3 marks

Given M is the midpoint of OC, find the vector AM in terms of a and b in simplest form.

  1. 1CB = 3/4 OA, so →BC = −3/4 a
  2. 2→OC = →OB + →BC = b − 3/4 a
  3. 3→OM = 1/2 →OC = 1/2 b − 3/8 a
  4. 4→AM = →AO + →OM = −a + 1/2 b − 3/8 a = −11/8 a + 1/2 b

Answer−11/8 a + 1/2 b

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Also searched as: 0580/42/O/N/25 · 0580_w25_qp_42 · 0580 w25 42 · question 18.
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