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

Answer: (B)

1

If the area of triangle is zero, then the points are collinear.

Points are collinear.

Point are $(p,o)(o,q)(i,q)$

$\Delta =\frac{1}{2}\left[p\right(q-1)-0(1-0)+1(0-q\left)\right]$

$\Rightarrow \frac{1}{2}\left[p\right(q-1)-q]$

$\Rightarrow \frac{1}{2}\left[p\right(q-1)-q]$

$\Rightarrow \frac{1}{2}[pq-(p+q\left)\right]=o$

$\Rightarrow pq=p+q\Rightarrow \frac{p+q}{pq}=1$

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