Question

If the three points a(a, 0) (0,b) (1,1) are collinear than prove that 1/a+1/b =1​

Answer 1

Step-by-step explanation:

Given,

Three points (a, 0) (0,b) (1,1) are collinear.

To Prove :-

$\frac{1}{a} + \frac{1}{b} = 1$

Proof:-

We know that,

if 3 points are collinear,

then,

the area swept by them is zero sq. units.

Therefore,

we get,

$= > \frac{1}{2} (a(b - 1) - 0(0 - 1) + 1(0 - b)) = 0 \\ \\ = >a(b - 1) - 0(0 - 1) + 1(0 - b) = 0 \\ \\ = > ab - a - b = 0 \\ \\ = > a + b = ab \\ \\ = > \frac{a + b}{ab} = \frac{ab}{ab} \\ \\ = > \frac{a}{ab} + \frac{b}{ab} = 1 \\ \\ = > \frac{1}{a} + \frac{1}{b} = 1$

Hence,

Proved