2026 PCSS P1 Q26

2026 PCSS P1 Q26

Secondary 4
5 marks

A plot of land is in the shape of a quadrilateral \(PQRS\), such that \(QR=8\text{ cm}\), angle \(PQR=81^\circ\) and \(PS=RS=9.8\text{ cm}\). \(PQ\) has been drawn for you.

  1. Construct the quadrilateral.[2]
  2. Construct the perpendicular bisector of \(PQ\).[1]
  3. Construct the angle bisector of \(QPR\).[1]
  4. The point \(X\) is equidistant away from \(P\) and \(Q\), nearer to \(PQ\) than \(PR\).
    Mark and label a possible placement of \(X\).[1]

Solution:

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Answer:(a)–(c) Construction shown (d) \(X\) on the perpendicular bisector of \(PQ\), nearer \(PQ\) than \(PR\)

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