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# If three points (h, 0), (a, b) and (0, k) lie on a line, show that a/h+b/k=1.

Q: 13         If three points  $(h,0),(a,b)$  and  $(0,k)$  lie on a line, show that   $\frac{a}{h}+\frac{b}{k}=1.$

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Points  $A(h,0),B(a,b)$  and  $C(0,k)$  lie on a line so by this we can say that their slopes are also equal
We know that
$Slope = m = \frac{y_2-y_1}{x_2-x_1}$

Slope of AB = $\frac{b-0}{a-h} = \frac{b}{a-h}$

Slope of AC = $\frac{k-b}{0-a} = \frac{k-b}{-a}$
Now,
Slope of AB = slope of AC
$\frac{b}{a-h} = \frac{k-b}{-a}$
$-ab= (a-h)(k-b)$
$-ab= ak -ab-hk+hb\\ ak +hb = hk$
Now divide both the sides by hk
$\frac{ak}{hk}+\frac{hb}{hk}= \frac{hk}{hk}\\ \\ \frac{a}{h}+\frac{b}{k} = 1$
Hence proved

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