Question

The distance of the point $\left(-2,3\right)$ from the line $x-y=5$ is

• A. $5\sqrt{2}$
• B. $2\sqrt{5}$
• C. $3\sqrt{5}$
• D. $5\sqrt{3}$

Answer 1

The correct option is A

$5\sqrt{2}$

Explanation for the correct answer:

Formula for distance of a point$\left(x_1,y_1\right)$ from a line $ax+by+c=0$is $\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}}$

The given line $x-y=5$ can be rewritten as $x-y-5=0$ and hence, $a=1,b=-1,c=-5$

So the distance of the point $\left(-2,3\right)$ from the line $x-y=5$ is:

$$\begin{gathered} =\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}} \\ =\frac{\left|-2-3-5\right|}{\sqrt{1+1}} \\ =\frac{10}{\sqrt{2}} \\ =5\sqrt{2} \end{gathered}$$

Hence, the correct answer is option (A).