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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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best_answer

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 

Posted by

Gautam harsolia

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