Solutions to this question by accurate drawing will not be accepted. The diagram (not drawn to scale

Question

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. Find the coordinates of $Q$.[5] $PQ$ meets the $y$-axis at $T$. Show that triangle $ORT$ is isosceles.[3] The point $S$ is such that $ORPS$ forms a parallelogram. Find the coordinates of $S$.[1] Find the area of the trapezium $OPQR$.[2]

Accepted Answer

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

2024 FMSS PRELIMS P1 Q12

2024 FMSS PRELIMS P1 Q12

Solution:

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