2025 IGCSE 0580 May/June P43 Q26

2025 IGCSE 0580 May/June P43 Q26

5 marks

The diagram shows a quadrilateral \(OXPY\) with diagonals meeting at \(T\).

\(\overrightarrow{OX}=3\mathbf a\) and \(\overrightarrow{OY}=12\mathbf b\).

  1. Find \(\overrightarrow{XY}\) in terms of \(\mathbf a\) and \(\mathbf b\).[1]
  2. \(XT:TY=1:2\) and \(\overrightarrow{YP}=5\mathbf a-2\mathbf b\).
    Find the ratio \(OT:TP\).[4]

Solution:

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Answer:(a) \(12\mathbf b-3\mathbf a\). (b) \(2:3\).

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