65 lines
1.8 KiB
TeX
65 lines
1.8 KiB
TeX
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\documentclass[a4paper,12pt]{article}
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\usepackage{myXsim}
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\author{Benjamin Bertrand}
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\title{Géométrie repérée - Cours}
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\date{2022-01-13}
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\pagestyle{empty}
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\begin{document}
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\maketitle
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\bigskip
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\section*{Distance entre deux points du plan}
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\begin{propriete}[Distance entre deux points]
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\begin{minipage}{0.5\linewidth}
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Soit $M (x_M; y_M)$ et $N (x_N; y_N)$ deux points quelconques. Alors la distance entre $M$ et $N$ se calcule
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\[
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NM = \sqrt{(x_M - x_N)^2 + (y_M - y_N)^2}
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\]
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\end{minipage}
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\hfill
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\begin{minipage}{0.4\linewidth}
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\begin{tikzpicture}[scale=1.2]
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\draw[->, very thick] (-1, 0) -- (4, 0);
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\draw[->, very thick] (0, -1) -- (0, 4);
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\draw (0, 0) node [below left] {0};
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\draw (1.3, 1.4) node {+} node [below left] {$M$};
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\draw (1.3, 0) node {+} node [below] {$x_M$};
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\draw (0, 1.4) node {+} node [left] {$y_M$};
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\draw[dashed] (1.3, 1.4) --(1.3, 0);
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\draw[dashed] (1.3, 1.4) --(0, 1.4);
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\draw (3.3, 3.4) node {+} node [above right] {$N$};
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\draw (3.3, 0) node {+} node [below] {$x_N$};
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\draw (0, 3.4) node {+} node [left] {$y_N$};
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\draw[dashed] (3.3, 3.4) --(3.3, 0);
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\draw[dashed] (3.3, 3.4) --(0, 3.4);
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\draw (1.3, 1.4) -- (3.3, 3.4);
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\draw (1.3, 1.4) -- node [midway, below] {$|x_M - x_N|$}
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(3.3, 1.4);
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\draw (3.3, 1.4) -- node [midway, below, sloped] {$|y_M - y_N|$}
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(3.3, 3.4);
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\end{tikzpicture}
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\end{minipage}
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\end{propriete}
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\paragraph{Exemple:} Distance entre $A (3; 4)$ et $B(-2; 0)$
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\[
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AB = \sqrt{(3 - (-2))^2 + (4 - 0)^2} = \sqrt{ 25 + 16 } = \sqrt{41} \approx 6.4
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\]
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\end{document}
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