Question

The ratio in which the line $3x + 4y + 2 = 0$ divides the distance between the lines $3x + 4y + 5 = 0$ and $3x + 4y - 5 = 0$ is

• A. $1 : 2$
• B. $3 : 7$
• C. $2 : 3$
• D. $2 : 5$

Answer 1

Answer: (B)

$3 : 7$

Answer 2

Distance between $3x + 4y + 2 = 0$ and $3x + 4y + 5 = 0$ is $\left|\frac{5-2}{\sqrt{\left(3\right)^{2}+\left(4\right)^{2}}}\right|=\frac{3}{5}$ Distance between $3x + 4y + 2 = 0$ and $3x + 4y - 5 = 0$ is $\left|\frac{-5-2}{\sqrt{3^{2}+\left(4\right)^{2}}}\right|=\frac{7}{5}$ $\therefore$ Line $3x + 4y + 2 = 0$ divides the distance between the lines $3x + 4y + 5 = 0$ and $3x + 4y - 5 = 0$ in the ratio $(3/5): (7/5) = 3:7$.