# Kelongs (SPM Additional Mathematics 2019)

Solution by scale drawing is not accepted.
Diagram 3 shows the positions of jetty $O$ and kelongs $K$, $L$, $R$, $S$, and $T$ in the sea. Kelong $L$ is situated $400 \mathrm{m}$ from jetty $O$ and kelong $R$ is situated $600 \mathrm{m}$ from jetty $O$ in the direction of $OL$. Kelong $S$ is situated $300 \mathrm{m}$ from jetty $O$ and kelong $T$ is situated $600 \mathrm{m}$ from kelong $S$ in the direction of $OS$. Kelongs $L$, $K$, and $T$ are situated on a straight line such that the distance of kelong $K$ from kelong $T$ is $5$ times its distance from kelong $L$.

If Joe uses a pair of binoculars to observe kelong $R$ from kelong $S$, determine whether kelong $R$ can be seen without being blocked by kelong $K$ or otherwise.

I tried to answer this question by using vectors and deciding whether the vectors $\overrightarrow{SK}$ and $\overrightarrow{KR}$ are collinear with vector $\overrightarrow{SR}$ or not. From my calculations, it seems that the answer should be that kelong $R$ can be seen from kelong $S$ without being blocked by kelong $K$, but I'm not sure whether my answer is right or wrong.

Note by Tan Chin Cheern
3 months, 2 weeks ago

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Menelaus’s Theorem will give you the answer. K would block the view if distance of kelong K from kelong T was 3 times its distance from kelong LL instead of 5 times.

- 2 months, 4 weeks ago