\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}

\author{Benjamin Bertrand}
\title{Géométrie repérée - Cours}
\date{2022-01-13}

\pagestyle{empty}

\begin{document}

\maketitle

\bigskip

\section*{Distance entre deux points du plan}


\begin{propriete}[Distance entre deux points]
    \begin{minipage}{0.5\linewidth}
        Soit $M (x_M; y_M)$ et $N (x_N; y_N)$ deux points quelconques. Alors la distance entre $M$ et $N$ se calcule
        \[
            NM = \sqrt{(x_M - x_N)^2 + (y_M - y_N)^2}
        \]
    \end{minipage}
    \hfill
    \begin{minipage}{0.4\linewidth}
        \begin{tikzpicture}[scale=1.2]
            \draw[->, very thick] (-1, 0) -- (4, 0);
            \draw[->, very thick] (0, -1) -- (0, 4);
            \draw (0, 0) node [below left] {0};

            \draw (1.3, 1.4) node {+} node [below left] {$M$};
            \draw (1.3, 0) node {+} node [below] {$x_M$};
            \draw (0, 1.4) node {+} node [left] {$y_M$};

            \draw[dashed] (1.3, 1.4) --(1.3, 0);
            \draw[dashed] (1.3, 1.4) --(0, 1.4);

            \draw (3.3, 3.4) node {+} node [above right] {$N$};
            \draw (3.3, 0) node {+} node [below] {$x_N$};
            \draw (0, 3.4) node {+} node [left] {$y_N$};

            \draw[dashed] (3.3, 3.4) --(3.3, 0);
            \draw[dashed] (3.3, 3.4) --(0, 3.4);

            \draw (1.3, 1.4) -- (3.3, 3.4);

            \draw (1.3, 1.4) -- node [midway, below] {$|x_M - x_N|$}
                (3.3, 1.4);
            \draw (3.3, 1.4) -- node [midway, below, sloped] {$|y_M - y_N|$}
                (3.3, 3.4);
        \end{tikzpicture}
    \end{minipage}
\end{propriete}

\paragraph{Exemple:} Distance entre $A (3; 4)$ et $B(-2; 0)$

\[
    AB = \sqrt{(3 - (-2))^2 + (4 - 0)^2} = \sqrt{ 25 + 16 } = \sqrt{41} \approx 6.4
\]


\end{document}
