Question

If points a,0, 0,b and 1,1 are collinear, then 1a+1b= A 1 B 2 C 0 D-1y​

Answer 1

Answer:

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.

$\color{indigo}\sf \frac{1}{2} [x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)] = 0$

$\color{orange} \sf \frac{1}{2} [a[b−1]+0[1−0]+1(0−b)]=0$

$\color{navy} \sf⇒ab−a−b=0$

$\color{blue} \sf⇒a+b=ab$

$\color{purple} \sf \therefore \: \frac{1}{a} + \frac{1}{b} = 1$