Question

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

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

Answer 1

Answer: (B)

Now, distance of origin from $4x + 2y - 9 = 0$ is
$\frac{| -9 |}{\sqrt{4^2+2^2}}=\frac{9}{\sqrt{20}}$
and distance of origin from $2x+ y + 6 = 0 $ is
$\frac{| 6 |}{\sqrt{2^2+1^2}}=\frac{6}{\sqrt{5}}$
Hence, the required ratio $=\frac{9/\sqrt{20}}{6/\sqrt{5}}=\frac{3}{4}$