Question
If the points $\mathrm{A}(h, 0), \mathrm{B}(0, \mathrm{k})$ and $\mathrm{C}(\mathrm{a}, \mathrm{b})$ lie on a line, then show that $\frac{a}{h}+\frac{b}{k}=1$.'
$\begin{array}{ll}\therefore \quad & \frac{k-0}{0-h}=\frac{b-k}{a-0} \\ \therefore \quad & a k=-h(b-k) \\ \therefore \quad & \frac{a}{h}=\frac{k-b}{k} \\ \therefore \quad & \frac{a}{h}=1-\frac{b}{k} \\ \therefore \quad & \frac{a}{h}+\frac{b}{k}=1\end{array}$
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