Question

If the points $(p,0)$, $(0,q)$ and $(1,1)$ are collinear, then $\frac{1}{p}+\frac{1}{q}$ is equal to:

• A. $-1$
• B. $1$
• C. $2$
• D. $0$

Answer 1

The correct option is B $1$

As the points are collinear, the slope of the line joining
any two points, should be same as the slope of the line joining two other
points.
Slope of the line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ $=$ $\frac{y_2-y_1}{x_2-x_1}$
So, slope of the line joining $(p,0),(0,q)=$ Slope of the line joining
$(0,q)$ and $(1,1)$
$\frac{q-0}{0-p}=\frac{1-q}{1-0}$
$-\frac{q}{p}=1-q$

Dividing both sides by $q$,
$-\frac{1}{p}=\frac{1}{q}-1$

$=>\frac{1}{p}+\frac{1}{q}=1$