The diagram (not drawn to scale) shows a right-angled triangle $PQR$ in which point $P$ is \((5,

Question

The diagram (not drawn to scale) shows a right-angled triangle $PQR$ in which point $P$ is $(5, 4)$ and point $R$ is $(9, 2)$. Point $S$ is $(-1.5, 11)$ and $PR$ is parallel to $SQ$. Find the equation of $PQ$.[2] Find the coordinates of $Q$.[3] Given that $T$ is a point on $QR$ extended such that $QT=10\sqrt{5}$ units, find the coordinates of $T$.[5]

Accepted Answer

(a) $y=2x-6$ (b) $Q=\left(\dfrac{13}{2},7\right)$ (c) $T=\left(\dfrac{33}{2},-13\right)$

2025 CGS PRELIMS P1 Q13

2025 CGS PRELIMS P1 Q13

Solution:

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