次の平面・軸・点に関して点 {\rm P}(1,\ 3,\ 2) と対称な点の座標を，それぞれ求めよ。
【解答】
\def\vX{1}\def\rX{-1}
\def\vY{3}\def\rY{-3}
\def\vZ{2}\def\rZ{-2}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{xy\,平面 \Rightarrow z\ の符号を変える！}\\
\\
& P(\vX,\ \vY,\ \colBX{bisque}{$\vZ$})
\quad\Rightarrow\quad
(\vX,\ \vY,\ \colBX{bisque}{$\rZ$})
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{1}\def\rX{-1}
\def\vY{3}\def\rY{-3}
\def\vZ{2}\def\rZ{-2}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{yz\,平面 \Rightarrow x\ の符号を変える！}\\
\\
& P(\colBX{bisque}{$\vX$},\ \vY,\ \vZ)
\quad\Rightarrow\quad
(\colBX{bisque}{$\rX$},\ \vY,\ \vZ)
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{1}\def\rX{-1}
\def\vY{3}\def\rY{-3}
\def\vZ{2}\def\rZ{-2}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{zx\,平面 \Rightarrow y\ の符号を変える！}\\
\\
& P(\vX,\ \colBX{bisque}{$\vY$},\ \vZ)
\quad\Rightarrow\quad
(\vX,\ \colBX{bisque}{$\rY$},\ \vZ)
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{1}\def\rX{-1}
\def\vY{3}\def\rY{-3}
\def\vZ{2}\def\rZ{-2}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{x\,軸 \Rightarrow y,\ z\ の符号を変える！}\\
\\
& P(\vX,\ \colBX{bisque}{$\vY$},\ \colBX{bisque}{$\vZ$})
\quad\Rightarrow\quad
(\vX,\ \colBX{bisque}{$\rY$},\ \colBX{bisque}{$\rZ$})
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{1}\def\rX{-1}
\def\vY{3}\def\rY{-3}
\def\vZ{2}\def\rZ{-2}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{y\,軸 \Rightarrow x,\ z\ の符号を変える！}\\
\\
& P(\colBX{bisque}{$\vX$},\ \vY,\ \colBX{bisque}{$\vZ$})
\quad\Rightarrow\quad
(\colBX{bisque}{$\rX$},\ \vY,\ \colBX{bisque}{$\rZ$})
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{1}\def\rX{-1}
\def\vY{3}\def\rY{-3}
\def\vZ{2}\def\rZ{-2}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{z\,軸 \Rightarrow x,\ y\ の符号を変える！}\\
\\
& P(\colBX{bisque}{$\vX$},\ \colBX{bisque}{$\vY$},\ \vZ)
\quad\Rightarrow\quad
(\colBX{bisque}{$\rX$},\ \colBX{bisque}{$\rY$},\ \vZ)
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{1}\def\rX{-1}
\def\vY{3}\def\rY{-3}
\def\vZ{2}\def\rZ{-2}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{原点 \Rightarrow x,\ y,\ z\ の符号を変える！}\\
\\
& P(\colBX{bisque}{$\vX$},\ \colBX{bisque}{$\vY$},\ \colBX{bisque}{$\vZ$})
\quad\Rightarrow\quad
(\colBX{bisque}{$\rX$},\ \colBX{bisque}{$\rY$},\ \colBX{bisque}{$\rZ$})
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan次の平面・軸・点に関して点 {\rm P}(3,\ 4,\ 5) と対称な点の座標を，それぞれ求めよ。
【解答】
\def\vX{3}\def\rX{-3}
\def\vY{4}\def\rY{-4}
\def\vZ{5}\def\rZ{-5}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{xy\,平面 \Rightarrow z\ の符号を変える！}\\
\\
& P(\vX,\ \vY,\ \colBX{bisque}{$\vZ$})
\quad\Rightarrow\quad
(\vX,\ \vY,\ \colBX{bisque}{$\rZ$})
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{3}\def\rX{-3}
\def\vY{4}\def\rY{-4}
\def\vZ{5}\def\rZ{-5}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{yz\,平面 \Rightarrow x\ の符号を変える！}\\
\\
& P(\colBX{bisque}{$\vX$},\ \vY,\ \vZ)
\quad\Rightarrow\quad
(\colBX{bisque}{$\rX$},\ \vY,\ \vZ)
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{3}\def\rX{-3}
\def\vY{4}\def\rY{-4}
\def\vZ{5}\def\rZ{-5}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{zx\,平面 \Rightarrow y\ の符号を変える！}\\
\\
& P(\vX,\ \colBX{bisque}{$\vY$},\ \vZ)
\quad\Rightarrow\quad
(\vX,\ \colBX{bisque}{$\rY$},\ \vZ)
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{3}\def\rX{-3}
\def\vY{4}\def\rY{-4}
\def\vZ{5}\def\rZ{-5}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{x\,軸 \Rightarrow y,\ z\ の符号を変える！}\\
\\
& P(\vX,\ \colBX{bisque}{$\vY$},\ \colBX{bisque}{$\vZ$})
\quad\Rightarrow\quad
(\vX,\ \colBX{bisque}{$\rY$},\ \colBX{bisque}{$\rZ$})
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{3}\def\rX{-3}
\def\vY{4}\def\rY{-4}
\def\vZ{5}\def\rZ{-5}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{y\,軸 \Rightarrow x,\ z\ の符号を変える！}\\
\\
& P(\colBX{bisque}{$\vX$},\ \vY,\ \colBX{bisque}{$\vZ$})
\quad\Rightarrow\quad
(\colBX{bisque}{$\rX$},\ \vY,\ \colBX{bisque}{$\rZ$})
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{3}\def\rX{-3}
\def\vY{4}\def\rY{-4}
\def\vZ{5}\def\rZ{-5}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{z\,軸 \Rightarrow x,\ y\ の符号を変える！}\\
\\
& P(\colBX{bisque}{$\vX$},\ \colBX{bisque}{$\vY$},\ \vZ)
\quad\Rightarrow\quad
(\colBX{bisque}{$\rX$},\ \colBX{bisque}{$\rY$},\ \vZ)
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan【解答】
\def\vX{3}\def\rX{-3}
\def\vY{4}\def\rY{-4}
\def\vZ{5}\def\rZ{-5}
\newcommand\colNS[2]{\textcolor{#1}{#2}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\newcommand\colFB[2]{\textcolor{#1}{\fbox{\scriptsize\bf\color{#1}#2}}}
\begin{align*}
& \colFB{red}{3次元} \quad \colNS{red}{x\,y\,z\ \cdots無い文字の符号を変える！}\\
\\
& \colNS{orange}{原点 \Rightarrow x,\ y,\ z\ の符号を変える！}\\
\\
& P(\colBX{bisque}{$\vX$},\ \colBX{bisque}{$\vY$},\ \colBX{bisque}{$\vZ$})
\quad\Rightarrow\quad
(\colBX{bisque}{$\rX$},\ \colBX{bisque}{$\rY$},\ \colBX{bisque}{$\rZ$})
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan
