If three point (h, 0), (a, b) and (0, k) lie on a line,

Question:

If three point (h, 0), (a, b) and (0, k) lie on a line, show that $\frac{a}{h}+\frac{b}{k}=1$

Solution:

If the points A (h, 0), B (a, b), and C (0, k) lie on a line, then

Slope of AB = Slope of BC

$\frac{b-0}{a-h}=\frac{k-b}{0-a}$

$\Rightarrow \frac{b}{a-h}=\frac{k-b}{-a}$

$\Rightarrow-a b=(k-b)(a-h)$

$\Rightarrow-a b=k a-k h-a b+b h$

$\Rightarrow k a+b h=k h$

On dividing both sides by kh, we obtain

$\frac{k a}{k h}+\frac{b h}{k h}=\frac{k h}{k h}$

$\Rightarrow \frac{a}{h}+\frac{b}{k}=1$

Hence, $\frac{a}{h}+\frac{b}{k}=1$

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