Question

The perpendicular distance of the straight line $12x+5y=7$ from the origin is given by

• A. $\frac{7}{13}$
• B. $\frac{12}{13}$
• C. $\frac{5}{13}$
• D. $\frac{1}{13}$

Answer 1

The correct option is A

$\frac{7}{13}$

Calculate the perpendicular distance of the straight line from the origin

We know that the length of the perpendicular from origin $(0,0)$ to the line $ax+by+c=0$ is

$d=\left|\frac{c}{\sqrt{(a^2+b^2)}}\right|$

Given line is $12x+5y=7$

So,

$d=\left|\frac{7}{\sqrt{({12}^2+5^2)}}\right|$

$=\left|\frac{7}{\sqrt{(144+25)}}\right|$

$=\left|\frac{7}{\sqrt{169}}\right|$

$=\frac{7}{13}$

Hence, the correct option is (A) $\frac{7}{13}$.