2026 CSS P1 Q25

2026 CSS P1 Q25

Secondary 4
4 marks

In the diagram, \(OWXY\) is a quadrilateral, \(\overrightarrow{OW}=5\mathbf{p}-2\mathbf{q}\), \(\overrightarrow{OY}=4\mathbf{p}+2\mathbf{q}\) and \(\overrightarrow{WX}=2\mathbf{p}+\mathbf{q}\).

  1. If \(M\) is a point such that \(\overrightarrow{OM}=10\mathbf{p}-4\mathbf{q}\), explain why \(O\), \(W\) and \(M\) lie on a straight line.[2]
  2. Is \(\triangle OYM\) similar to \(\triangle WXM\)? Explain your answer.[2]

Solution:

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Answer:(a) \(\overrightarrow{OM}=2\overrightarrow{OW}\), with common point \(O\). (b) Yes, by SAS similarity, scale factor \(2\).

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