Question

If the point (a,0),(0,b)and (1,1) are collinear ,then a+b=

Answer 1

Answer:

a+b=2

Explanation:

by distance formula,

(a-1)^2+(1)^2+(b-1)^2+(1)^2=(a-0)^2+(0-b)^2

a^2+1-2a +1+b^2+1-2b +1=a^2+b^2

-2a-2b +4=0

-2a-2b=-4

-2 (a+b)=-4

a+b=-4/-2

a+b=2

Answer 2

Given that three points are collinear, (a,o),(o,b) and (1,1)

Since the points are collinear, area of triangle formed by these points is equal to O.

$\sf \frac{1}{2} [x </p><p>1</p><p> </p><p> (y </p><p>2</p><p> </p><p> −y </p><p>3</p><p> </p><p> )+x </p><p>2</p><p> </p><p> (y </p><p>3</p><p> </p><p> −y </p><p>1</p><p> </p><p> )+x </p><p>3</p><p> </p><p> (y </p><p>1</p><p> </p><p> −y </p><p>2</p><p> </p><p> )]=0$

$\sf \frac{1}{2} </p><p> [a[b−1]+0[1−0]+1(0−b)]=0$

$\sf⇒ab−a−b = 0$

$\sf⇒a+b=ab$

$\sf∴ \color{blue} \frac{1}{a} + \frac{1}{b} = 1$