From 426f8ae89f9a9352a61b5847d1ceceec4107e724 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 25 Jan 2022 09:17:21 +0100 Subject: [PATCH] Feat: fin de la correction des exercices --- 2nd/10_Geometrie_reperee/exercises.tex | 127 ++++++++++++++++++++----- 2nd/10_Geometrie_reperee/index.rst | 7 +- 2nd/10_Geometrie_reperee/solutions.pdf | Bin 50165 -> 56251 bytes 3 files changed, 111 insertions(+), 23 deletions(-) diff --git a/2nd/10_Geometrie_reperee/exercises.tex b/2nd/10_Geometrie_reperee/exercises.tex index 3674b10..3df8445 100644 --- a/2nd/10_Geometrie_reperee/exercises.tex +++ b/2nd/10_Geometrie_reperee/exercises.tex @@ -195,27 +195,27 @@ % ---- étape 2 \begin{exercise}[subtitle={Distance sur une droite}, step={2}, origin={dMeedC}, topics={Géométrie repérée}, tags={Coordonnées, distance}, mode={\faIcon{search}}] - On considère une droite munie d'un repère et deux points $A$ et $B$ de cette droite. + On considère une droite munie d'un repère et deux points $A$ et $B$ de cette droite. - Comme la droite est munie d'un repère, on peut considérer les abscisses $x_A$ et $x_B$ de ces deux points. + Comme la droite est munie d'un repère, on peut considérer les abscisses $x_A$ et $x_B$ de ces deux points. - \begin{enumerate} - \item Dans cette question, on suppose que $x_A = 2$ et $x_B = 9$. - \begin{center} - \begin{tikzpicture} - \foreach \x in {0, 1, ..., 10} {% - \draw (\x, 0.1) -- (\x, -0.1) node [below] {\x}; - } - \draw[->] (-0.5, 0) -- (10.5, 0); - \draw (2, 0) node {x} node [above] {$A$}; - \draw (9, 0) node {x} node [above] {$B$}; - \end{tikzpicture} - \end{center} - Proposer une formule utilisant $x_A$ et $x_B$ pour calculer la distance $AB$. - \item Même question pour $x_A = 58$ et $x_B = 9$. - \item Même question pour $x_A = 3$ et $x_B = -2$. - \item On suppose que $x_A$ et $x_B$ peuvent prendre n'importe quelle valeur. Déterminer une façon de calculer la distance $AB$ en utilisant $x_A$ et $x_B$. - \end{enumerate} + \begin{enumerate} + \item Dans cette question, on suppose que $x_A = 2$ et $x_B = 9$. + \begin{center} + \begin{tikzpicture} + \foreach \x in {0, 1, ..., 10} {% + \draw (\x, 0.1) -- (\x, -0.1) node [below] {\x}; + } + \draw[->] (-0.5, 0) -- (10.5, 0); + \draw (2, 0) node {x} node [above] {$A$}; + \draw (9, 0) node {x} node [above] {$B$}; + \end{tikzpicture} + \end{center} + Proposer une formule utilisant $x_A$ et $x_B$ pour calculer la distance $AB$. + \item Même question pour $x_A = 58$ et $x_B = 9$. + \item Même question pour $x_A = 3$ et $x_B = -2$. + \item On suppose que $x_A$ et $x_B$ peuvent prendre n'importe quelle valeur. Déterminer une façon de calculer la distance $AB$ en utilisant $x_A$ et $x_B$. + \end{enumerate} \end{exercise} \begin{exercise}[subtitle={Bilan sur distance sur une droite}, mode={\faIcon{users}}, step={2}, origin={dMeedC}, topics={Géométrie repérée}, tags={Coordonnées, distance}] @@ -457,13 +457,15 @@ \end{exercise} \begin{solution} - \begin{itemize} + \begin{enumerate} \item Longueur $AC$ \[ AC = \sqrt{(-50 - 50)^2 + (100 - (-100))^2} = \sqrt{(-100)^2 + 200^2} = \sqrt{50 000} \] - \item - \end{itemize} + \item Il faut calculer les longueurs $AB$ et $BC$ puis appliquer le théorème de Pythagore. C'est la même rédaction que la question 3 de l'exercice 11. Le triangle est rectangle. + \item Il faut calculer les longueurs $AD$ et $DC$ puis appliquer le théorème de Pythagore. C'est la même rédaction que la question 3 de l'exercice 11. Le triangle n'est pas rectangle. + \item On sait que $ABCD$ est un quadrilatère et le triangle $ACD$ n'est pas rectangle. Or un carré est un quadrilatère qui a 4angles droits et 4côté de même longueur. Donc $ABCD$ n'est pas un carré. + \end{enumerate} \end{solution} % ---- étape 4 @@ -511,6 +513,47 @@ \end{enumerate} \end{exercise} +\begin{solution} + \begin{enumerate} + \item Les points de l'ensemble $(a)$ vérifie $y=2x$ donc leur ordonnée doit être deux fois plus grand que leur abscisse. + \begin{itemize} + \item Pour le point $U$ + \[ + 2x = 2\times 2 = 4 = y + \] + Donc le point $U$ appartient à $(a)$ + \item Pour le point $V$ + \[ + 2x = 2\times 1 = 2 \neq -1 = y + \] + Donc le point $V$ n'appartient pas à $(a)$ + \item Pour le point $W$ + \[ + 2x = 2\times -2 = -4 = y + \] + Donc le point $W$ appartient à $(a)$ + \item Pour le point $X$ + \[ + 2x = 2\times 0 = 0 = y + \] + Donc le point $X$ appartient à $(a)$ + \end{itemize} + \item ~ + + \begin{tikzpicture} + \repere{-5}{5}{-5}{5} + + \draw (2, 4) node {x} node [below left] {$U$}; + \draw (1, -1) node {x} node [below left] {$V$}; + \draw (-1, -2) node {x} node [below left] {$W$}; + \draw (0, 0) node {x} node [above left] {$X$}; + + \draw(-2, -4) node [above left] {$(a)$}; + \draw[domain=-2.5:2.5] plot(\x, {2*\x}); + \end{tikzpicture} + \end{enumerate} +\end{solution} + \begin{exercise}[subtitle={Ensemble $y = -x$}, step={4}, origin={Création}, topics={Géométrie repérée}, tags={Coordonnée, équation, ensemble}, mode={\faIcon{tools}}] On note $(b)$ l'ensemble des points tel que $y = -x$. Cette ensemble est une droite. @@ -526,4 +569,44 @@ \end{enumerate} \end{exercise} +\begin{solution} + \begin{enumerate} + \item Les points de l'ensemble $(b)$ vérifie $y=-x$ donc leur ordonnée doit être opposé à leur abscisse. + \begin{itemize} + \item Pour le point $U$ + \[ + -x = 2 = -2 \neq 4 = y + \] + Donc le point $U$ n'appartient pas à $(b)$ + \item Pour le point $V$ + \[ + - x = -1 = y + \] + Donc le point $V$ appartient à $(b)$ + \item Pour le point $W$ + \[ + -x = -(-1) = 1 \neq -2 = y + \] + Donc le point $W$ n'appartient pas à $(b)$ + \item Pour le point $X$ + \[ + -x = - 0 = 0 = y + \] + Donc le point $X$ appartient à $(b)$ + \end{itemize} + \item ~ + + \begin{tikzpicture} + \repere{-5}{5}{-5}{5} + + \draw (2, 4) node {x} node [below left] {$U$}; + \draw (1, -1) node {x} node [below left] {$V$}; + \draw (-1, -2) node {x} node [below left] {$W$}; + \draw (0, 0) node {x} node [above right] {$X$}; + + \draw(-4, 4) node [above right] {$(b)$}; + \draw[domain=-5:5] plot(\x, {-\x}); + \end{tikzpicture} + \end{enumerate} +\end{solution} diff --git a/2nd/10_Geometrie_reperee/index.rst b/2nd/10_Geometrie_reperee/index.rst index b95bf5b..592ba17 100644 --- a/2nd/10_Geometrie_reperee/index.rst +++ b/2nd/10_Geometrie_reperee/index.rst @@ -2,7 +2,7 @@ Géométrie repérée ################# :date: 2022-01-10 -:modified: 2022-01-15 +:modified: 2022-01-25 :authors: Benjamin Bertrand :tags: Géométrie, Repère :category: 2nd @@ -41,6 +41,11 @@ L'étape 5 suit l'étape 4. :alt: Tout en 1! +.. image:: ./solutions.pdf + :height: 200px + :alt: Solution des exercices techniques + + Étape 1: Coordonnée du milieu ----------------------------- diff --git a/2nd/10_Geometrie_reperee/solutions.pdf b/2nd/10_Geometrie_reperee/solutions.pdf index d04243483579f4190ae716ac4dde7f341fe44a33..260605d4c2499782f6c6a958b37c6ee225cb89b6 100644 GIT binary patch delta 31328 zcmV*2KzG0OhXcE}1F)qL4Bsr~-5l2W9}7=e*|V_`Br60nH!?JnF)kE;?Oe;Q8@UnP 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