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(Utilisation du plan cartsien pour tablir des relations entre diffrents points ou groupes de points: droites, figures...)$$recO$$($$Reco$$Object 13/0 . N. NI . NI `+S ]/ QH $$recO$$)$$Reco$$ParagrapxZ5 Q  Plan cartsien$$recO$$x$$Reco$$Object 3515  ^ ^  ^ R+S) O a $$recO$$[.$$Reco$$ParagrapL a  Coordonnes (x,y)$$recO$$N$$Reco$$Object 5739  p p  p c+S _ t $$recO$$HS$$Reco$$Paragrap[ t  Distance entre deux points$$recO$$$$Reco$$Object 7953~~c~cc+S __$$recO$$4$$Reco$$Paragrapp[  Pente$$recO$$p$$Reco$$Object 9;7755c+S _1$$recO$$V$$Reco$$Paragrap[  Point de partage d'un segment$$recO$$8$$Reco$$Object ;=90+*+*o+*oD+Sb A.0l$$recO$$Q$$Reco$$ParagrapG50       ! ' ( * + . / Connaissant deux points P1(x1, y1) et P2(x2, y2) on dtermine la pente m de la droite passant par ces deux points l'aide du rapport:$$recO$$2$$Reco$$Object =?;4ww?w?NNdH`x I~:$$recO$$$$Reco$$Object ?A=8|!'|!'c"Q|!'c"Q**/  G !5S"F$$recO$$-$$Reco$$Object AC?5 ""#7"#7D+S1 A"#1$$recO$$r$$Reco$$Paragrap "  On remarque que la distance entre les deux points reprsente l'hypotnuse d'un triangle. En appliquant le thorme de Pythagore on obtient la formule suivante:$$recO$$ v$$Reco$$Object C!EA9 ""%#?"%#?3HG  "##9$$recO$$'$$Reco$$Object E#GC.  v! v!&HG   i!$$recO$$$$Reco$$Object G%IE,   !C  !CD+S A !=$$recO$$ $$Reco$$Paragrapq   Le plan cartsien est form de deux axes qui dcoupent l'espace et permettent d'attribuer des coordonnes chacun des points du plan.$$recO$$N$$Reco$$Object I'KG1T T q! T q! c+S& _U p!$$recO$$JX$$Reco$$Paragrapp[\   Points$$recO$$p!$$Reco$$Object K)MI7  #f+S !b$$recO$$$$Reco$$Paragrap^  Point milieu d'un segment$$recO$$4>$$Reco$$Object M+OK?$3m$W $W mm+HG 3m'W $$recO$$0$$Reco$$Paragrapzm'TT  On peut trouver les coordonnes du point milieu d'un segment en dterminant les points milieux des deux segments exprimant la variation en x et en y.T Les coordonnes du point milieu d'un segment quelconque sont donnes par la formule:$$recO$$zD$$Reco$$Object O-QM@  !v !v22-HG  / !n$$recO$$9$$Reco$$Object Q/SO/3X3Xc+S _2T$$recO$$D$$Reco$$Paragrapp[  Droite$$recO$$pv$$Reco$$Object S1UQ,R+S< O$$recO$$!$$Reco$$Paragrap~L  Forme fonctionnelle$$recO$$~$$Reco$$Object U3WS,TTR+S< OQ$$recO$$@$$Reco$$ParagrapxL  Forme gnrale$$recO$$xv$$Reco$$Object W5YU,wwwR+S< Oz$$recO$$z$$Reco$$ParagrapzLz  Forme symtrique$$recO$$zʸ$$Reco$$Object Y7[W*444llBHH h9$$recO$$=$$Reco$$Object [9]Y&4 4 4 a+SE \9$$recO$$(G$$Reco$$Paragrapi>((  Avantages: Associe la prvision. m= pente b = ordonne l'origine abscisse l'origine= -b/m Inconvnients:( ne s'applique pas la droite verticale.$$recO$$6$$Reco$$Object ];_[&444a+SQ \9$$recO$$ $$Reco$$Paragrap9%%  Avantages:F Permet de dfinir dans le plan cartsien toutes les droites possibles. Ordonne l'origine=-C/B Abscisse l'origine= -C/A pente= -A/B Inconvnients:% Aucune proprit dfinie directement.$$recO$$" $$Reco$$Object _=a]&44 K4 Ka+SU \9 D$$recO$$Vp$$Reco$$Paragrap7>22  Avantages: a= abscisse l'origine b= ordonne l'origine pente= -b/a Inconvnients:2 Ne peut dfinir les droites passant par l'origine.$$recO$$$$Reco$$Object a?c_*UUOHH {Q$$recO$$$$Reco$$Object cAea*5]5]SHH$ 1Z$$recO$$$$Reco$$Object eCgc,c+SDB _ {$$recO$$N$$Reco$$Paragrap[   Informations pour la dterminer$$recO$$t$$Reco$$Object gEie.W+SH T$$recO$$'$$Reco$$ParagrapQ  En connaissant deux couples.$$recO$$$$Reco$$Object iGkg*,W+SH *T$$recO$$N$$Reco$$ParagrapQ%% % En connaissant un couple et la pente.$$recO$$~($$Reco$$Object kImi*<+SM 9$$recO$$ap$$Reco$$Paragrap(yy  1) Avec le taux on dtemine m.y 2) On remplace y et x dans la rgle de la fonction affine par la valeur du point et on isole b pour dterminer sa valeur.$$recO$$($$Reco$$Object mKok.;;U+SK Q7la val$$recO$$B$$Reco$$Paragrap|| 4 1) On calcul la pente selon la formule m=y2-y1/x2-x1 2) Avec la pente on dtemine m.| 3) On remplace y et x dans la rgle de la fonction affine par la valeur du point et on isole b pour en dterminer la valeur.$$recO$$wD$$Reco$$Object oMqm7gggc+S _kla val$$recO$$l$$Reco$$Paragrap[k   Distance d'un point une droite$$recO$$$$Reco$$Object qOso:IIE+S5 BFla val$$recO$$$$Reco$$Paragrapj        ! 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