Question

If the points $(a,0),(0,b)$ and $(1,1)$ are collinear, then $\frac{1}{a}+\frac{1}{b}$ is:

• A. $-1$
• B. $1$
• C. $0$
• D. $2$

Answer 1

The correct option is B $1$

Since the given points are collinear, they do not form a triangle, which means area of the triangle is Zero.
Hence, substituting the points $(x_1,y_1)=(a,0)$ ; $(x_2,y_2)=(0,b)$ and $(x_3,y_3)=(1,1)$ in the area formula, we get
$\left|\frac{a(b-1)+0(1-0)+1(0-b)}{2}\right|=0$
$\Rightarrow ab-a-b=0$
$\Rightarrow a+b=ab$
Dividing by $ab,$ we get
$\frac{1}{a}+\frac{1}{b}=1$