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0580/43 Oct/Nov 2025, Question 26: Vector Geometry

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

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The question, in short

Use vectors in parallelogram ABCD with AB = m, AD = p, F dividing BC 4:1 and E dividing AD 1:2 to find EF and CG.

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

Part (a) · 3 marks

Express vector EF using m and p, given BF = 4FC and AE:ED = 1:2.

  1. 1→EF = →EA + →AB + →BF
  2. 2= −1/3 p + m + 4/5 p
  3. 3= m + 7/15 p

Answerm + 7/15 p

Part (b) · 2 marks

With EF and DC extended to meet at G, express vector CG using m and/or p.

  1. 1Triangles FCG and EDG are similar (FC is parallel to ED)
  2. 2FC = 1/5 p and ED = 2/3 p, so CG : DG = 1/5 : 2/3 = 3 : 10
  3. 3DG = DC + CG, so DC : CG = 7 : 3 and CG = 3/7 of DC
  4. 4→DC = m, so →CG = 3/7 m

Answer3/7 m

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Also searched as: 0580/43/O/N/25 · 0580_w25_qp_43 · 0580 w25 43 · question 26.
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