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100644 index 0000000..ae80983 --- /dev/null +++ b/2nd/10_Geometrie_reperee/3B_distance.tex @@ -0,0 +1,64 @@ +\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} diff --git a/2nd/10_Geometrie_reperee/3B_val_abs.pdf b/2nd/10_Geometrie_reperee/3B_val_abs.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0099f606933c7643f29e3fa49450c880ee4a7c70 GIT binary patch literal 55840 zcmce+bF6UR5+!)`UE8*8+qTW`+O}=mwr$(CZTsH&z3zUQp3Eej`QyEvoRf_@J7;B8 zs&?%x5_w@!8U|VxNRqjw;WbERe0qFaLkmc5Zb&+1cRLe&I(0ci3lk$JNIE5FL#O{S zBWmkl4M`^`XzPZrMgNaI1O5MabRg;eweml{Vt}NRF>rD)|Hp#iAB%t1|MmXILea$0 z*4e?x#1Wt6pBY6+I%yLdQztWg1{VDP)&AMV+{($s0iRCP%D~A)*u==z*aVW77t+zm z!NkBC(rsfAZbqJbW)BDe>>Kb7(!|F2f35t}``53t{j>3Z2Lk(l3IfM}4Fbcz$oY@Z z!0<21|2sS|F#g9t{P&!R;Xme0jQ`^JzrzIMzexX&xDzAOe-FgJg5ZA!1nYkf#J@cE zKLUd3e`n&~;hUYE@qfne|8w}h)|7DEWJT_|RNGTE$0S@!mGwMJ@F+9D$M#B%|0k|{?u0!nzbK8Sqkiw3qFz^=RmKY zfP3I80e^VQ{0N(4pN92nNu*6hQ_Z{tb)!NBBkC~QZnZ>~ 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