点到平面的距离(B009)

问题

点 $M$ $(x_{0}, y_{0}, z_{0})$ 到平面 $Ax$ $+$ $By$ $+$ $Cz$ $=$ $0$ 的距离 $d$ $=$ $?$

选项

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

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

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

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



显示答案

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