Question

A straight line through the origin $O$ meets the parallel lines $4x+2y=9$ and $2x+y+6=0$ at $P$ and $Q$ respectively. the point $O$ divides the segment $PQ$ in the ratio

• A. $1:2$
• B. $3:4$
• C. $2:1$
• D. $4:3$

Answer 1

The correct option is B $3:4$


$OP=\left|\frac{0-9}{\sqrt{16+4}}\right|=\frac{9}{2\sqrt{5}}$
$OQ=\frac{6}{\sqrt{5}}$
$\Rightarrow \frac{OP}{OQ}=\frac{\frac{9}{2\sqrt{5}}}{\frac{6}{\sqrt{5}}}=\frac{3}{4}$