Question

The length of perpendicular from $(3,1)$ on line $4x+3y+20=0$, is

• A. $6$
• B. $7$
• C. $5$
• D. $8$

Answer 1

The correct option is B

$7$

Explanation for correct option:

Given equation of the line is $4x+3y+20=0$

The given point is $(3,1)$

We know that the perpendicular distance to a line $ax+by+c=0$ from point $\left(x_1,y_1\right)$ is given by $d=\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}}$

Therefore the perpendicular distance of the line $4x+3y+20=0$ from the point $(3,1)$ is

$$\begin{gathered} d=\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}} \\ =\frac{\left|4·3+3·1+20\right|}{\sqrt{4^2+3^2}} \\ =\frac{35}{5} \\ =7 \end{gathered}$$

Hence, option B is correct .