2024 FMSS PRELIMS P1 Q12

2024 FMSS PRELIMS P1 Q12

11 marks

Solutions to this question by accurate drawing will not be accepted.

The diagram (not drawn to scale) shows a trapezium \(OPQR\) in which \(PQ\) is parallel to \(OR\) and \(\angle ORQ = 90^\circ\). The coordinates of \(P\) and \(R\) are \((-4, 3)\) and \((4, 2)\) respectively and \(O\) is the origin.

  1. Find the coordinates of \(Q\).[5]
  2. \(PQ\) meets the \(y\)-axis at \(T\). Show that triangle \(ORT\) is isosceles.[3]

The point \(S\) is such that \(ORPS\) forms a parallelogram.

  1. Find the coordinates of \(S\).[1]
  2. Find the area of the trapezium \(OPQR\).[2]

Solution:

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Answer:(i) \(Q=(2,6)\). (ii) \(OT=RT=5\), so \(\triangle ORT\) is isosceles (shown). (iii) \(S=(-8,1)\). (iv) \(25\) square units.

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