Question

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

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

Answer 1

The correct option is B

3 : 7

Here, in all equations the coefficient of x is same.

It means all the lines have same slope.

So, all the lines are parallel.

Now, the distance between the line $3x+4y+2=0$ and $3x+4y+5=0$ is given by

$\frac{|2-5|}{\sqrt{3^2+4^2}}$

$=\frac{3}{\sqrt{25}}=\frac{3}{5}$

Again, the distance between the line $3x+4y+2=0$ and $3x+4y-5=0$ is given by

$\frac{|2+5|}{\sqrt{3^2+4^2}}$

$=\frac{7}{\sqrt{25}}=\frac{7}{5}$

Hence, the ratio is given by

$\frac{3}{5}:\frac{7}{5}$

$=3:7$

Hence, the correct answer is option (b).