二维直角坐标系上点到直线的距离(B009)

问题

在二维直角坐标系中,点 $M$ $(x_{0}, y_{0})$ 到直线 $Ax$ $+$ $By$ $+$ $C$ $=$ $0$ 的距离 $d$ $=$ $?$

选项

[A].   $d$ $=$ $\frac{\left|A x_{0}+B y_{0}+C\right|}{A^{2}+B^{2}}$

[B].   $d$ $=$ $\frac{\left|A x_{0}+B y_{0}+C\right|}{\sqrt{A+B}}$

[C].   $d$ $=$ $\frac{A x_{0}+B y_{0}+C}{\sqrt{A^{2}+B^{2}}}$

[D].   $d$ $=$ $\frac{\left|A x_{0}+B y_{0}+C\right|}{\sqrt{A^{2}+B^{2}}}$



显示答案

$d$ $=$ $\frac{\left|\textcolor{orange}{A} \textcolor{cyan}{x_{0}}+\textcolor{orange}{B} \textcolor{cyan}{y_{0}}+\textcolor{orange}{C}\right|}{\sqrt{\textcolor{orange}{A}^{\textcolor{red}{2}}+\textcolor{orange}{B}^{\textcolor{red}{2}}}}$