2026 NASS P1 Q10

2026 NASS P1 Q10

Secondary 4
7 marks

In the diagram, \(AB\), \(BC\), \(CD\), \(DA\), \(AC\), and \(DB\) are walkways connecting four blocks of apartments. An urban planner plans to build some facilities at \(K\), \(L\), \(P\) and \(Q\), which are midpoints of \(AD\), \(BC\), \(BD\) and \(AC\) respectively.

Show that

  1. \(PK=LQ\),[3]
  2. \(KL\) bisects \(PQ\).[4]

Solution:

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Answer:(a) \(PK=LQ=\dfrac12AB\). (b) \(KPLQ\) is a parallelogram, so \(KL\) bisects \(PQ\).

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