Question

The length of perpendicular from a point $(1,2)$ to the straight line $3x+4y+4=0$

• A. $5$
• B. $3$
• C. $\frac{7}{5}$
• D. None of these

Answer 1

The correct option is B

$3$

Explanation for correct option:

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

The given point is $(1,2)$

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 $3x+4y+4=0$ from the point $(1,2)$ is

$$\begin{gathered} d=\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}} \\ =\frac{\left|3·1+4·2+4\right|}{\sqrt{3^2+4^2}} \\ =\frac{15}{5} \\ =3 \end{gathered}$$

Hence, option B is correct