arrow_back What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}\right)$ and the line $a x+b y+c=0$ in $R^2$?

Question

What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}\right)$ and the line $a x+b y+c=0$ in $R^2$?

Answer 1

In $R^{2}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}\right)$ and the line $a x+b y+c=0$ is $$ D=\frac{\left|a x_{0}+b y_{0}+c\right|}{\sqrt{a^{2}+b^{2}}} $$