(iii) If S divides CA in the ratio $K : 1$, what is the value of K, where point A is $(200, 800)$?

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Step 1: $C(-600, 0)$, $A(200, 800)$, $S(-200, 400)$. S divides CA in ratio $k : 1$. Using section formula: $-200 = \frac{k(200) + 1(-600)}{k + 1} \Rightarrow -200(k + 1) = 200k - 600 \Rightarrow -200k - 200 = 200k - 600 \Rightarrow 400 = 400k \Rightarrow k = 1$

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