exo30.tex

Sur la carte de France, on a placé différentes villes. {\bf On
  laissera apparaître tous les traits nécessaires.}
\begin{center}
\unitlength=0.6mm
\begin{picture}(180,170)
%Carte de France
\path(100,161)(102,160)(102,157)(105,154)(108,155)(110,154)(111,150)(112.5,150)(114.5,147)
(116,147)(119,147.5)(121,147)(121,145)(120,141.5)(123,140)(125,142)(128,144)(129,143)(128,141)
(130,138)(134,136)(137,134)(141,133.5)(143,133)(145,133)(148,132)
(150,130)(153,128)(159,127)(160,127)(162,126)(165,126)(168,125)(170,124)(170.5,123)(169,121)
(167,118)(166,115)(165,112)(164,110)(164,101)(163,98)(162,97)(160,96)(158,97)(156.5,95)
(157,93)(155,90)(151,87)(147,80)(146,78)(146,75)
(145,73)(148,75)(150,77)(152,78)(153,78)(155,76)(155.5,73)(157,70)(157,68)(156,66)
(157,64)(160,61)(160.5,59)(160,58)(156,55)(155,54.5)(154,54)(156,52)(158,50)(160,48)(160,47)
(158.5,43)(159,40)(163,37)(166,37)(166,37)(167.5,36.5)(168,34)(167,31)(166,29)
(164,28)(162,26)(156,21)(157,19)(156,18)(155,17.5)(153,18)(152,18)(150,17)(147,17)(145,17.5)
(142,18)(140,19)(138,20)(137.5,21)(136.5,20)(135,19.5)(134,21)(135,22)(136.5,23)(134,25)
(133.5,23)(132,22)(130,21)(128.5,21)(128,22)
(128.5,23.5)(127,25)(126,24.5)(126,23)(124.5,22)(122,24)(120,24)(118,22)(115,20)(111,19)
(109,17)(107.5,16.5)(107,15)(107.5,13)(107.5,12)(108,10)(108.5,8)(110,6)(110.5,5)(110,4)
(107.5,3)(105,2.5)(102,2)(98.5,3)(95,2)(93,3)
(91,5)(90,6)(90,7)(89,8)(86,9)(84,10)(83,10)(80,11)(79,11)(76,10)(70,9.5)(65,10)
(63,11.5)(60,12)(57,14)(55,14)(52,17.5)(50,16)(48.5,17)(48.5,19)(49,20)(47,21)(46,22)
(46,23)(46.5,24.5)(49,30)
(50,34)(52,40)(52.5,44)(53,45)(55.5,46.5)(55,48)(54,47)(53,47)(52.5,48)(53,49)(54,60)(55,61)
(56,61.5)(57,61)(61,53)(60,59)(59,61)(55,64)(55,66)(56,70)(55,73)(55,75)(53,76)(52,77)
(48,79)(46,83)
(44,85)(43.5,86)(44.5,89)(43,91)(43.5,92)(45,93.5)(43,93)(42,93)(39,94)(39,95)
(40,97.5)(37.5,99.5)(34,99.5)(33,100)(33,102)(25,104)(22,106)(20,104)(19,104)(18,105)(18,107)
(15,109)(15,111)(19.5,111)(18,112)(16,112)
(15,113)(16,114)(18,114)(18.5,115)(15,115)(14,115.5)(14,119)(16,120)(20,121)(22.5,121.5)
(25,120.5)(28.5,121)(31,123)(32,123)(35,122)(40,117)(42,119)(43,119)(45,118)(47,118)(49,119)
(50,119)(52,117)(55,117)(55,118)(54,118)
(53,119)(52.5,120)(53,122.5)(52,129)(50,131.5)(49.5,136)(51,137)(52,137)(53,136)(55,136)
(57,136.5)(57.5,135)(58,130)(60,131)(61,131)(68,130)(69,128)(77,132)(73,132)(72,133)(73,135)
(75,136)(85,140)(88,142)(90,144)(91,144.5)(90,146)(90.5,150)(90,154)(91,156)(92,157)(100,161)
%Garonne
\path(83.5,10)(83.5,12)(82.5,13)(81.5,15.5)(80,17)(82,19)(85,22)(87.5,25)(86,30)(83.5,35)(82,36)
(80,37)(77,38)(76,40)(75,42)(73,43)(70,45)(67,46)(65,47)(63,50)(61,53)
%Rhône
\path(132,22)(131,25)(130,27)(129,28)
\path(126,24.5)(126,26)(129,28)(129,30)(131,33)(131.5,34)(131.5,35)(131,36)(129.5,39)(130,45)
(131,50)(131.5,55)(130,58)(131.5,65)(131,67)(131.5,68)(133,67.5)(138,68)(140,64)(142.5,67)
(142.5,71)(143,72)(145,73)
%Seine
\path(129.5,97)(128,100)(126,103)(125,108)(122,111)(119.5,112.5)(118,116)(116,117)(115,116.5)
(113,116)(108,114)(107,113.5)(105,114)(104,116)(102,117)(100,120)(99,122)(99,123)(98,123)
(97,122.5)(96,123.5)(95.5,124)(95,124)(94,124.5)(93,125)(92,124.5)(91,126)(89,126)(88,128)
(87,130)(85.5,130.5)(85,132)(84,132)(83,131.5)(82.5,133)(81,132)(80,133)(77,132)
%Loire
\path(124.5,49.5)(124,48.5)(123,48)(122,48)(121,49)(120,50)(119.5,52)(119.5,53)(120,55)(122,57)
(122.5,58)(123.5,60)(123,62)(122.5,65)(121,69)(121.5,75)(121,77)(120,78)(117.5,80)(116,82)
(115,84)(114,85)(111,86)(108,88)(107,90)(107,92)(106,95)(105,99)(103,101)(100,103)
(98,104)(96.5,104.5)(95,104)(92,103)(90,101)(88,99)(85,97)(83,96)(80,95.5)(78,95)(76,94)
(74.5,93)(73,92)(72,91.5)(71,92)(70,92.5)(69,93)(67,95)(66,96)(63,95.5)(60,95)
(57,94)(55,93)(53,91.5)(50,92)(45,93.5)
\put(112,145){\circle{1}}\put(103,145){\small Lille}
\put(161,118.5){\circle{1}}\put(151,119.5){\small Strasbourg}
\put(16.5,117.5){\circle{1}}\put(17.5,117.5){\small Brest}
\put(69,50){\circle{1}}\put(65,51){\small Bordeaux}
\put(113,131.5){\circle{1}}\put(105,132.5){\small Laon}
\put(117,109.5){\circle{1}}\put(107,110.5){\small Troyes}
\put(100,120){\circle{1}}%Paris
\put(100,87.5){\circle{1}}\put(90,89){\small Bourges}
\put(111,78.5){\circle{1}}\put(100.5,79.5){\small Moulins}
\put(118.5,49){\circle{1}}%Le Puy
\put(140.5,21.5){\circle{1}}%Marseille
\put(84,130){\circle{1}}\put(74,127){\small Rouen}
\put(10,10){\rnode{A}{}\kern1cm\rnode{B}{}}
\ncline{|-|}{A}{B}
\naput{100~km}
\end{picture}
\end{center}
\par
\begin{myenumerate}
\item Place le point $P$ pour Paris, $M$ pour Marseille et $L$ pour Le
  Puy.\par Trace en vert la droite $(PL)$. Trace en bleu la droite
  $(RM)$. Que remarque-t-on ?
\item Est-ce que les villes de Bordeaux, Bourges et Troyes sont
  alignées ? Justifie la réponse.
\item Les villes de Brest, Nantes, Marseille sont alignées.
\par Les villes de Strasbourg, Troyes et Nantes sont alignées.
\par Place le point $N$ qui représente la ville de Nantes. Explique ta
méthode.
\item Place le point $S$ qui représente la ville de Sète : elle se
  situe au bord de la Méditerranée et les villes de Lille, Laon et
  Sète sont alignées.
\item Carcassonne se situe à 300~km au sud de Bordeaux et à 300~km à
  l'ouest de Marseille.\par Place le point $C$ représentant la ville
  de Carcassonne.
\end{myenumerate}