%
%	gbb60166@gmail.com	https://unilab.gbb60166.jp/prekou/prekou.htm
%
% aspectratio= は 1610, 169, 149, 54, 32 の中から選べる（省略時は 43）
% C:\texlive\2024\texmf-dist\tex\latex\beamer\beamer.cls
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfpagemode=FullScreen},aspectratio=169]{beamer}
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfstartview={XYZ null null 8.00}},aspectratio=169]{beamer}
\documentclass[20pt,dvipdfmx,usepdftitle=false,aspectratio=169]{beamer}
% pdfの栞の字化けを防ぐ
%\AtBeginDvi{\special{pdf:tounicode EUC-UCS2}}
% テーマ
\usetheme{Copenhagen}
% navi. symbolsは目立たないが，dvipdfmxを使うと機能しないので非表示に
\setbeamertemplate{navigation symbols}{} 
\usepackage{bxdpx-beamer,pxjahyper,minijs}
%\usepackage{graphicx}
%\usepackage{tkokugo,furikana,tsayusen,shiika,sfkanbun,jdkintou,plext}
\usepackage{type1cm}
\usepackage[deluxe]{otf}
%\usepackage{tikzsymbols}
%\usepackage[dvipdfmx]{graphicx}%
\def\pgfsysdriver{pgfsys-dvipdfmx.def}%（graphicxパッケージを使用しない場合はこの行を有効に）
%\def\pgfsysdriver{pgfsys-dvips.def}%デフォルト
%\usepackage[e]{esvect}
\usepackage{tikz}%（これで、pgfとpgfforが読み込まれます。）
%\usepackage{tikz-3dplot}
\usetikzlibrary{calc}
%\usetikzlibrary{arrows.meta,patterns,angles,intersections,backgrounds}
%\usepackage{animate}
%\usepackage{pgfplots}
%\pgfplotsset{compat=newest}
%\pgfplotsset{compat=newest, every axis/.append style={line width=1pt}}
%\PassOptionsToPackage{dvipdfmx}{graphicx}
\nofiles

\hypersetup{% Jul 18 2023
	pdftitle={プレ高数学科（LaTeX Beamer で汎用PDFプレゼンを作る）},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/prekou/prekou.htm}
	}

% フォントはお好みで
%\usepackage{txfonts}

\mathversion{bold}
\renewcommand{\familydefault}{\sfdefault}
\renewcommand{\seriesdefault}{bx}
\renewcommand{\kanjifamilydefault}{\gtdefault}
\renewcommand{\kanjiseriesdefault}{bx}
\setbeamerfont{title}{size=\normalsize,series=\bfseries}
\setbeamerfont{frametitle}{size=\normalsize,series=\bfseries}
\setbeamertemplate{frametitle}[default][center]
\usefonttheme{professionalfonts}

% 参考にしたURL
% http://windom.phys.hirosaki-u.ac.jp/fswiki/wiki.cgi?page=LaTeX+Beamer%A4%C7%A5%D7%A5%EC%A5%BC%A5%F3%A5%C6%A1%BC%A5%B7%A5%E7%A5%F3

\newcommand{\Slash}[1]{\ooalign{\hfil\kern-3pt／\hfil\crcr$#1$}}
\everymath{\displaystyle}

\newcommand{\maruwaku}[1]{\begin{tikzpicture}[scale=0.7, baseline={([yshift=-22pt] current bounding box.north)}]
\filldraw[color=CUDBlue, line width=1pt, rounded corners=2pt] (-0.1,0)--(2.1,0)--(2.1,1.1)--(-0.1,1.1)--cycle;
\draw(1,0.5) node[white]{#1};
\end{tikzpicture}
}

\setbeamersize{text margin left=5mm,text margin right=5mm}
\fboxrule=0.8pt

\makeatletter
\newcommand{\hooklen}[2]{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
%■等号付き不等号 by 美文書作成入門
\newcommand{\myleqq}{\mathrel{\mathpalette\gl@align<}}
\newcommand{\mygeqq}{\mathrel{\mathpalette\gl@align>}}
\newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
	\ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\makeatother

% カラーユニバーサルデザインを調べたつもりだがあまり自信がありません
% http://www.fukushihoken.metro.tokyo.jp/kiban/machizukuri/kanren/color.files/colorudguideline.pdf
% http://jfly.iam.u-tokyo.ac.jp/colorset/

% ■ アクセントカラー小面積を目立たせる高彩度色
\definecolor{CUDRed}{RGB}{255,75,0}
\definecolor{CUDGreen}{RGB}{3,175,122}
\definecolor{CUDBlue}{RGB}{0,90,255}
\definecolor{CUDCyan}{RGB}{77,196,255}
\definecolor{CUDMagenta}{RGB}{153,0,153}
\definecolor{CUDYellow}{RGB}{255,241,0}
\definecolor{CUDBrown}{RGB}{128,64,0}

\definecolor{CUDOrange}{RGB}{246,170,0}

% ■ ベースカラー広い面積の塗り分けに用いる低・中彩度色
\definecolor{CUDPink}{RGB}{255,202,191}
\definecolor{CUDBrightGreen}{RGB}{119,217,168}
\definecolor{CUDLime}{RGB}{216,242,85}
\definecolor{CUDCream}{RGB}{255,255,128}
\definecolor{CUDBrightCyan}{RGB}{191,228,255}
%\definecolor{CUD}{RGB}{}%

\setbeamercolor{CUDBrightGreen}{fg=black,bg=CUDBrightGreen!50}
\setbeamercolor{CUDBrightCyan}{fg=black,bg=CUDBrightCyan}
\setbeamercolor{CUDCream}{fg=black,bg=CUDCream!75}

%\setbeamercolor{frametitle}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{palette primary}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{frametitle}{bg=CUDOrange}
%\setbeamercolor{palette primary}{bg=CUDOrange}
%\setbeamercolor{frametitle}{bg=CUDCyan!25,fg=black}
%\setbeamercolor{palette primary}{bg=CUDCyan!25,fg=black}
%\setbeamercolor{frametitle}{bg=CUDCream!75,fg=black!80}
%\setbeamercolor{palette primary}{bg=CUDCream!75,fg=black!80}

\newcommand{\myfrac}[2]{\mathchoice%■ 修正 Oct 8,2023
	{%\fontsize{20}{20}\selectfont%	\displaystyle
		\frac{\raisebox{-.6ex}{\(#1\)}}{\raisebox{.4ex}{\(#2\)}}}%
	{\textstyle{\frac{#1}{#2}}}%	\textstyle
	{%\fontsize{13}{13}\selectfont%	\scriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	{%\fontsize{11}{11}\selectfont%	\scriptscriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	}


\begin{document}

\title{プレ高数学科}\author{gbb60166}

%■ 本文と数式モードの間に挿入される空白スペース
%\mathsurround=0pt
%■ \( \log\log \)でlogとlogの間に挿入される細スペース（省略形は \,）
%\thinmuskip=3mu
%■ \( a+b \)で+の前後に挿入される中スペース（省略形は \>）
\medmuskip=2mu plus 1mu minus 1mu
%■ \( x=5 \)で=の前後に挿入される太スペース（省略形は \;）
%\thickmuskip=5mu plus 5mu
% mu は math units の省略で長さの単位

%■■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■■



%\end{document}
%■■■■■■■■■■■■■　完成品　■■■■■■■■■■■■■■

\begin{frame}[t]
\frametitle{点\( (3,4) \)と直線\( 2x+y-5=0 \)の距離？}
\vspace*{-13pt}
\centerline{%
\begin{tikzpicture}[scale=1, >=stealth,
	baseline={([yshift=-20pt] current bounding box.north)}]
%\footnotesize
%\foreach \x in {-1,...,6}{\draw[gray] (\x,-1)--(\x,6);}
%\foreach \y in {-1,...,6}{\draw[gray] (-1,\y)--(6,\y);}
\foreach \x in {-1,...,6}{\draw[gray] (\x,-1)--(\x,6)
					(-1,\x)--(6,\x);}
\draw[->,very thick](-1,0)--(6,0);
\draw[->,very thick](0,-1)--(0,6);
\draw[CUDBlue,very thick](-0.5,6)--(3,-1);
\draw(5,1.6) node[CUDBlue]{\(2x+y-5=0\)};
%\draw(2.9,4.5) node[CUDGreen]{\((3,4)\)};
\fill[CUDGreen](3,4) circle(3pt) node[above]{\((3,4)\)};
\visible<2->{\draw[teal,very thick]($(1,3)!12pt!(3,4)$)--
		($(1,3)!12pt!(3,4)!12pt!-90:(3,4)$)--($(1,3)!12pt!(3,-1)$);
	\draw[<->,CUDRed,line width=3pt](3,4)--(1,3);
	}
\end{tikzpicture}
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{公式（点と直線の距離）}
点\( (x_1,y_1) \)と直線\( ax+by+c=0 \)の距離は

\bigskip
\[ \myfrac{\ \bigl|\, a x_1+b y_1+c \,\bigr|\ }{\sqrt{a^2+b^2 \ }} \]
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{ことばで書いた方が分かりやすいですか？}
点 \colorbox{CUDCream}{\((\raisebox{-2pt}{\textcolor{CUDMagenta}{★}},
	\raisebox{-2pt}{\textcolor{CUDOrange}{■}})\)} と
	直線\( \colorbox{CUDBrightCyan}{%
		\(\raisebox{-2pt}{\textcolor{CUDRed}{●}}x+
	\raisebox{-2pt}{\textcolor{CUDGreen}{◆}}y+
	\raisebox{-2pt}{\textcolor{CUDBlue}{▲}}\)}=0 \)の\\[1ex]
距離は

\vskip-3ex
\[ \myfrac{\ \Bigl|\,\text{\colorbox{CUDBrightCyan}{直線の式の左辺} に\ 
	\colorbox{CUDCream}{点の座標} を代入}\,\Bigr|\ 
	}{
	\sqrt{\text{\textcolor{CUDRed}{\footnotesize
		\shortstack{$x$の前\\[-1pt]の数字}}\ }^2
	\raisebox{6pt}{\(+\)}\ 
	\text{\textcolor{CUDGreen}{\footnotesize
		\shortstack{$y$の前\\[-1pt]の数字}}\ }^2 \ }} \]
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{点と直線の距離（例題$1$）}
% ■こんなに色を多用することは妥当なのか？
点\alt<2->{\( (\colorbox{CUDMagenta}{\textcolor{white}{$3$}},
		\colorbox{CUDOrange}{\textcolor{white}{$4$}}) \)}
	{\( (\hooklen{\colorbox{CUDMagenta}{$3$}}{3},
		\hooklen{\colorbox{CUDOrange}{$4$}}{4}) \)}と
直線\alt<2->{\( \textcolor{CUDRed}{2}
	\colorbox{CUDMagenta}{\textcolor{white}{$x$}}
	+ \textcolor{CUDGreen}{1}\colorbox{CUDOrange}{\textcolor{white}{$y$}}
	\textcolor{CUDBlue}{{}-5}=0 \)}
		{\( 2\hooklen{\colorbox{CUDMagenta}{$x$}}{x}
		+ \phantom{1}\hooklen{\colorbox{CUDOrange}{$y$}}{y}-5=0 \)}の
		距離は\pause

\vskip-2ex
\begin{eqnarray*}
& & \myfrac{\ \bigl|\, \textcolor{CUDRed}{2}\times
	\colorbox{CUDMagenta}{\textcolor{white}{$3$}}
	+\textcolor{CUDGreen}{1}\times
		\colorbox{CUDOrange}{\textcolor{white}{$4$}}
	\textcolor{CUDBlue}{{}-5} \,\bigr|\ }{
	\sqrt{\textcolor{CUDRed}{2}^2+\textcolor{CUDGreen}{1}^2 \,}}\\[1ex]\pause
&=& \myfrac{\ \bigl|\, \hooklen{2\times\colorbox{CUDMagenta}{$3$}}{6}+
	\hooklen{1\times\colorbox{CUDOrange}{$4$}}{4}-5 \,\bigr|\ }{ \sqrt{5}}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{点と直線の距離（例題$1$）}
\vspace*{-3ex}
\begin{eqnarray*}
&=& \myfrac{\ \bigl|\, 6+4-5 \,\bigr|\ }{ \sqrt{5}}\pause
	=\myfrac{\ \bigl|\, 5 \,\bigr|\ }{ \sqrt{5}}
	=\myfrac{\ 5 \ }{ \sqrt{5}}\\[1ex]
&=& \myfrac{\ 5 \textcolor{CUDRed}{\times\!\sqrt{5}} }{
		\sqrt{5}\textcolor{CUDRed}{\times\!\sqrt{5}}}
	=\myfrac{5\sqrt{5}}{5}=\sqrt{5}\ \text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{点と直線の距離（例題$2$）}
点\( (-1,2) \)と直線\( 3x-5y+6=0 \)の距離は\pause

\vskip-2ex
\begin{eqnarray*}
& & \myfrac{\ \bigl|\, 3\times(-1)-5\times2+6 \,\bigr|\ }{
	\sqrt{3^2+(-5)^2 \,}}\\[1ex]\pause
&=& \myfrac{\ \bigl|\,\hooklen{3\times(-1)}{-3}
	-\hooklen{5\times2}{10}+6 \,\bigr|\ }{ \sqrt{34}}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{点と直線の距離（例題$2$）}
\vspace*{-3ex}
\begin{eqnarray*}
&=& \myfrac{\ \bigl|\, -3-10+6 \,\bigr|\ }{ \sqrt{34}}\pause
	=\myfrac{\ \bigl|\, -7 \,\bigr|\ }{ \sqrt{34}}
	=\myfrac{\ 7 \ }{ \sqrt{34}}\\[1ex]
&=& \myfrac{\ 7 \textcolor{CUDRed}{\times\!\sqrt{34}} }{
		\sqrt{34}\textcolor{CUDRed}{\times\!\sqrt{34}}}
	=\myfrac{7\sqrt{34}}{34}\ \text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{点と直線の距離（例題$3$）}
点\( (7,-5) \)と直線\( y=\myfrac{\,3\,}{4}x+2 \)の距離の場合は

\vskip-2ex
\begin{eqnarray*}
\textcolor{CUDRed}{4\times} y &=& 
	\Bigl(\myfrac{\,3\,}{4}x+2\Bigr)\textcolor{CUDRed}{\times4}\\[1ex]
4y &=& 3x+8 \\
0 &=& 3x-4y+8 \qquad\text{だから}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{点と直線の距離（例題$3$）}
点\( (7,-5) \)と直線\( 3x-4y+8=0 \)の距離を求めることになる。

\vskip4ex
\centerline{\( \myfrac{\,49\,}{5} \)\ \□答}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\end{document}

