{"id":1930,"date":"2023-11-22T22:05:10","date_gmt":"2023-11-22T21:05:10","guid":{"rendered":"http:\/\/localhost:8080\/maxblog\/?p=1930"},"modified":"2023-11-22T23:44:23","modified_gmt":"2023-11-22T22:44:23","slug":"representer-et-caracteriser-les-droites-du-plan","status":"publish","type":"post","link":"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/","title":{"rendered":"Repr\u00e9senter et caract\u00e9riser les droites du plan"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"1930\" class=\"elementor elementor-1930\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7d71a4a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7d71a4a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-389cd7d\" data-id=\"389cd7d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a8169f1 elementor-widget elementor-widget-spacer\" data-id=\"a8169f1\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7643655 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7643655\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f297427\" data-id=\"f297427\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-361d80f elementor-widget elementor-widget-heading\" data-id=\"361d80f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-heading-title elementor-size-xl\">Repr\u00e9senter et caract\u00e9riser les droites du plan<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c2bda19 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c2bda19\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d178bc4\" data-id=\"d178bc4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-de06178 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"de06178\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cc24190\" data-id=\"cc24190\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b7c611b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b7c611b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9a7e2c2\" data-id=\"9a7e2c2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fffe349 nc-justify-text elementor-widget elementor-widget-text-editor\" data-id=\"fffe349\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#Introduction\" >Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#Cours\" >Cours<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#1_Vecteur_directeur_dune_droite\" >1. Vecteur directeur d&rsquo;une droite<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#2_Equation_de_droite\" >2. \u00c9quation de droite<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#Methodes\" >M\u00e9thodes<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#1_Determiner_une_equation_de_droite_a_partir_de_donnees_fournies\" >1. D\u00e9terminer une \u00e9quation de droite \u00e0 partir de donn\u00e9es fournies<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#2_Determiner_la_pente_ou_un_vecteur_directeur_dune_droite_donnee_par_une_equation_ou_une_representation_graphique\" >2. D\u00e9terminer la pente ou un vecteur directeur d\u2019une droite donn\u00e9e par une\n\u00e9quation ou une repr\u00e9sentation graphique<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#3_Tracer_une_droite_connaissant_son_equation_cartesienne_ou_reduite\" >3. Tracer une droite connaissant son \u00e9quation cart\u00e9sienne ou r\u00e9duite<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#4_Etablir_que_trois_points_sont_alignes_ou_non\" >4. \u00c9tablir que trois points sont align\u00e9s ou non<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#5_Determiner_si_deux_droites_sont_paralleles_ou_secantes\" >5. D\u00e9terminer si deux droites sont parall\u00e8les ou s\u00e9cantes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.maxdecours.com\/maxblog\/representer-et-caracteriser-les-droites-du-plan\/#6_Resoudre_un_systeme_de_deux_equations_lineaires_a_deux_inconnues_determiner_le_point_dintersection_de_deux_droites_secantes\" >6. R\u00e9soudre un syst\u00e8me de deux \u00e9quations lin\u00e9aires \u00e0 deux inconnues,\nd\u00e9terminer le point d\u2019intersection de deux droites s\u00e9cantes<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"Introduction\"><\/span>Introduction<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">En g\u00e9om\u00e9trie analytique, les droites du plan cart\u00e9sien sont\nsouvent d\u00e9finies par des \u00e9quations et peuvent \u00eatre caract\u00e9ris\u00e9es par plusieurs\npropri\u00e9t\u00e9s, dont leur vecteur directeur, leur \u00e9quation et leur pente. Ces\nconcepts sont fondamentaux pour comprendre et travailler avec des droites dans\nun contexte math\u00e9matique.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h1><span class=\"ez-toc-section\" id=\"Cours\"><\/span>Cours<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Dans ce cours, le plan est muni d\u2019un rep\u00e8re orthonorm\u00e9.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"1_Vecteur_directeur_dune_droite\"><\/span>1. Vecteur directeur d&rsquo;une droite<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Un vecteur directeur d&rsquo;une droite est un vecteur qui indique\nla direction de la droite dans le plan. Il est d\u00e9fini par deux points <span class=\"katex-eq\" data-katex-display=\"false\">A(x_1,\ny_1)<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">B(x_2, y_2)<\/span> de la droite tels que :<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vec{AB} = (x_2 &#8211; x_1, y_2 &#8211; y_1) <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Tous les vecteurs colin\u00e9aires \u00e0 <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{AB}<\/span> sont\ndes vecteurs directeurs de la m\u00eame droite. Deux droites sont parall\u00e8les si et\nseulement si leurs vecteurs directeurs sont colin\u00e9aires.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"2_Equation_de_droite\"><\/span>2. \u00c9quation de droite<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">a. <b>\u00c9quation cart\u00e9sienne<br style=\"mso-special-character:\nline-break\">\n<br style=\"mso-special-character:line-break\">\n<\/b><\/p>\n\n<p class=\"MsoNormal\">L&rsquo;\u00e9quation cart\u00e9sienne d&rsquo;une droite est de la forme <span class=\"katex-eq\" data-katex-display=\"false\">Ax\n+ By + C = 0<\/span>, o\u00f9 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span>\nsont des r\u00e9els constants. Cette \u00e9quation permet de d\u00e9terminer si un point <span class=\"katex-eq\" data-katex-display=\"false\">M(x,\ny)<\/span> appartient \u00e0 la droite : le point <span class=\"katex-eq\" data-katex-display=\"false\">M<\/span> est sur la droite\nsi et seulement si <span class=\"katex-eq\" data-katex-display=\"false\">Ax + By + C = 0<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">b. <b>\u00c9quation r\u00e9duite<br style=\"mso-special-character:line-break\">\n<br style=\"mso-special-character:line-break\">\n<\/b><\/p>\n\n<p class=\"MsoNormal\">L&rsquo;\u00e9quation r\u00e9duite d&rsquo;une droite est une simplification de\nl&rsquo;\u00e9quation cart\u00e9sienne et s&rsquo;\u00e9crit sous la forme <span class=\"katex-eq\" data-katex-display=\"false\">y = mx + p<\/span>, o\u00f9 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span>\nest le coefficient directeur (ou la pente) et <span class=\"katex-eq\" data-katex-display=\"false\">p<\/span> est l&rsquo;ordonn\u00e9e \u00e0\nl&rsquo;origine. Cette forme est particuli\u00e8rement pratique pour repr\u00e9senter\ngraphiquement une droite.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>3. Pente (ou coefficient directeur) d\u2019une droite non\nparall\u00e8le \u00e0 l\u2019axe des ordonn\u00e9es<\/b><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">La pente, ou le coefficient directeur, d&rsquo;une droite est un\nindicateur de son inclinaison par rapport \u00e0 l&rsquo;axe des abscisses. Elle est\nd\u00e9finie uniquement pour les droites qui ne sont pas parall\u00e8les \u00e0 l&rsquo;axe des\nordonn\u00e9es. La pente <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> est donn\u00e9e par :<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> m = \\frac{y_2 &#8211; y_1}{x_2 &#8211; x_1} <\/span> o\u00f9 <span class=\"katex-eq\" data-katex-display=\"false\">\n(x_1, y_1) <\/span> et <span class=\"katex-eq\" data-katex-display=\"false\"> (x_2, y_2) <\/span> sont deux points distincts\nde la droite.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><b>Interpr\u00e9tations de la pente :<br style=\"mso-special-character:\nline-break\">\n<br style=\"mso-special-character:line-break\">\n<\/b><\/p>\n\n<p class=\"MsoNormal\">&#8211; Si <span class=\"katex-eq\" data-katex-display=\"false\">m &gt; 0<\/span>, la droite est ascendante.<\/p>\n\n<p class=\"MsoNormal\">&#8211; Si <span class=\"katex-eq\" data-katex-display=\"false\">m &lt; 0<\/span>, la droite est descendante.<\/p>\n\n<p class=\"MsoNormal\">&#8211; Si <span class=\"katex-eq\" data-katex-display=\"false\">m = 0<\/span>, la droite est horizontale.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h1><span class=\"ez-toc-section\" id=\"Methodes\"><\/span>M\u00e9thodes<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"1_Determiner_une_equation_de_droite_a_partir_de_donnees_fournies\"><\/span>1. D\u00e9terminer une \u00e9quation de droite \u00e0 partir de donn\u00e9es fournies<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">a. <b>Deux points <span class=\"katex-eq\" data-katex-display=\"false\">A(x_1, y_1)<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">B(x_2,\ny_2)<\/span><\/b> :<br style=\"mso-special-character:line-break\">\n<br style=\"mso-special-character:line-break\">\n<\/p>\n\n<p class=\"MsoNormal\">La pente <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> de la droite est donn\u00e9e par :<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> m = \\frac{y_2 &#8211; y_1}{x_2 &#8211; x_1} <\/span><\/p>\n\n<p class=\"MsoNormal\"><br>\nL&rsquo;\u00e9quation r\u00e9duite de la droite est donc :<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> y = m(x &#8211; x_1) + y_1 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">b. <b>Un point <span class=\"katex-eq\" data-katex-display=\"false\">A(x_1, y_1)<\/span> et un vecteur\ndirecteur <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{v} = (a, b)<\/span><\/b>&nbsp;:<\/p>\n\n<p class=\"MsoNormal\"><br>\nLa pente <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> est <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{b}{a}<\/span>, et l&rsquo;\u00e9quation r\u00e9duite\nest :<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> y = \\frac{b}{a}(x &#8211; x_1) + y_1 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">c. <b>Un point <span class=\"katex-eq\" data-katex-display=\"false\">A(x_1, y_1)<\/span> et la pente <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span><\/b>\n:<\/p>\n\n<p class=\"MsoNormal\"><br>\nL&rsquo;\u00e9quation r\u00e9duite est simplement :<br style=\"mso-special-character:line-break\">\n<br style=\"mso-special-character:line-break\">\n<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> y = m(x &#8211; x_1) + y_1 <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"2_Determiner_la_pente_ou_un_vecteur_directeur_dune_droite_donnee_par_une_equation_ou_une_representation_graphique\"><\/span>2. D\u00e9terminer la pente ou un vecteur directeur d\u2019une droite donn\u00e9e par une\n\u00e9quation ou une repr\u00e9sentation graphique<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">a. <b>\u00c9quation r\u00e9duite <span class=\"katex-eq\" data-katex-display=\"false\">y = mx + p<\/span><\/b> :<\/p>\n\n<p class=\"MsoNormal\"><br>\nLa pente est directement donn\u00e9e par <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span>, et un vecteur directeur\npossible est <span class=\"katex-eq\" data-katex-display=\"false\">(1, m)<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">b. <b>\u00c9quation cart\u00e9sienne <span class=\"katex-eq\" data-katex-display=\"false\">Ax + By + C = 0<\/span><\/b>\n:<\/p>\n\n<p class=\"MsoNormal\">La pente est <span class=\"katex-eq\" data-katex-display=\"false\">-\\frac{A}{B}<\/span> et un vecteur\ndirecteur possible est <span class=\"katex-eq\" data-katex-display=\"false\">(B, -A)<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">c. <b>Repr\u00e9sentation graphique<\/b> :<\/p>\n\n<p class=\"MsoNormal\"><br>\nChoisir deux points <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> sur la droite, puis\ncalculer la pente <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> comme pr\u00e9c\u00e9demment. Le vecteur <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{AB}<\/span>\nsera un vecteur directeur.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"3_Tracer_une_droite_connaissant_son_equation_cartesienne_ou_reduite\"><\/span>3. Tracer une droite connaissant son \u00e9quation cart\u00e9sienne ou r\u00e9duite<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">a. <b>\u00c9quation r\u00e9duite <span class=\"katex-eq\" data-katex-display=\"false\">y = mx + p<\/span><\/b> :<\/p>\n\n<p class=\"MsoNormal\"><br>\nTracer le point d&rsquo;ordonn\u00e9e \u00e0 l&rsquo;origine <span class=\"katex-eq\" data-katex-display=\"false\">p<\/span> puis utiliser la pente <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span>\npour trouver un autre point. Relier les points.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">b. <b>\u00c9quation cart\u00e9sienne <span class=\"katex-eq\" data-katex-display=\"false\">Ax + By + C = 0<\/span><\/b>\n:<\/p>\n\n<p class=\"MsoNormal\"><br>\nTrouver deux points <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> en substituant des\nvaleurs de <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> et r\u00e9soudre pour <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span>, ou vice versa.\nRelier les points.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"4_Etablir_que_trois_points_sont_alignes_ou_non\"><\/span>4. \u00c9tablir que trois points sont align\u00e9s ou non<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Trois points <span class=\"katex-eq\" data-katex-display=\"false\">A(x_1, y_1)<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">B(x_2, y_2)<\/span>,\net <span class=\"katex-eq\" data-katex-display=\"false\">C(x_3, y_3)<\/span> sont align\u00e9s si les pentes <span class=\"katex-eq\" data-katex-display=\"false\">AB<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">BC<\/span>\nsont \u00e9gales, c&rsquo;est-\u00e0-dire si :<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\frac{y_2 &#8211; y_1}{x_2 &#8211; x_1} = \\frac{y_3 &#8211; y_2}{x_3 &#8211;\nx_2} <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"5_Determiner_si_deux_droites_sont_paralleles_ou_secantes\"><\/span>5. D\u00e9terminer si deux droites sont parall\u00e8les ou s\u00e9cantes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Deux droites <span class=\"katex-eq\" data-katex-display=\"false\">d_1: y = m_1x + p_1<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">d_2:\ny = m_2x + p_2<\/span> sont:<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>Parall\u00e8les<\/b> si <span class=\"katex-eq\" data-katex-display=\"false\">m_1 = m_2<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">p_1\n\\neq p_2<\/span>.<br style=\"mso-special-character:line-break\">\n<br style=\"mso-special-character:line-break\">\n<\/p>\n\n<p class=\"MsoNormal\">&#8211; <b>S\u00e9cantes<\/b> si <span class=\"katex-eq\" data-katex-display=\"false\">m_1 \\neq m_2<\/span>.<\/p>\n\n<p class=\"MsoNormal\"><br>\n&#8211; <b>Confondues<\/b> si <span class=\"katex-eq\" data-katex-display=\"false\">m_1 = m_2<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">p_1 = p_2<\/span>.<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<h2><span class=\"ez-toc-section\" id=\"6_Resoudre_un_systeme_de_deux_equations_lineaires_a_deux_inconnues_determiner_le_point_dintersection_de_deux_droites_secantes\"><\/span>6. R\u00e9soudre un syst\u00e8me de deux \u00e9quations lin\u00e9aires \u00e0 deux inconnues,\nd\u00e9terminer le point d\u2019intersection de deux droites s\u00e9cantes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">Pour r\u00e9soudre le syst\u00e8me :<\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{cases} y = m_1x + p_1 \\\\ y = m_2x + p_2\n\\end{cases} <\/span><\/p>\n\n<p class=\"MsoNormal\">&nbsp;<\/p>\n\n<p class=\"MsoNormal\">On \u00e9galise les deux \u00e9quations pour trouver <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>,\npuis on substitue <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> dans une des \u00e9quations pour trouver <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span>.\nLe point d&rsquo;intersection est alors <span class=\"katex-eq\" data-katex-display=\"false\">I(x, y)<\/span>.<\/p>\n\n\n\n\n\n<style>@font-face\n\t{font-family:\"Cambria Math\";\n\tpanose-1:2 4 5 3 5 4 6 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:roman;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-536870145 1107305727 0 0 415 0;}@font-face\n\t{font-family:Calibri;\n\tpanose-1:2 15 5 2 2 2 4 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:swiss;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-536859905 -1073732485 9 0 511 0;}@font-face\n\t{font-family:\"Calibri Light\";\n\tpanose-1:2 15 3 2 2 2 4 3 2 4;\n\tmso-font-charset:0;\n\tmso-generic-font-family:swiss;\n\tmso-font-pitch:variable;\n\tmso-font-signature:-469750017 -1073732485 9 0 511 0;}p.MsoNormal, li.MsoNormal, div.MsoNormal\n\t{mso-style-unhide:no;\n\tmso-style-qformat:yes;\n\tmso-style-parent:\"\";\n\tmargin:0cm;\n\tmso-pagination:widow-orphan;\n\tfont-size:12.0pt;\n\tfont-family:\"Calibri\",sans-serif;\n\tmso-ascii-font-family:Calibri;\n\tmso-ascii-theme-font:minor-latin;\n\tmso-fareast-font-family:Calibri;\n\tmso-fareast-theme-font:minor-latin;\n\tmso-hansi-font-family:Calibri;\n\tmso-hansi-theme-font:minor-latin;\n\tmso-bidi-font-family:\"Times New Roman\";\n\tmso-bidi-theme-font:minor-bidi;\n\tmso-fareast-language:EN-US;}h1\n\t{mso-style-priority:9;\n\tmso-style-unhide:no;\n\tmso-style-qformat:yes;\n\tmso-style-link:\"Titre 1 Car\";\n\tmso-style-next:Normal;\n\tmargin-top:12.0pt;\n\tmargin-right:0cm;\n\tmargin-bottom:0cm;\n\tmargin-left:0cm;\n\tmso-pagination:widow-orphan lines-together;\n\tpage-break-after:avoid;\n\tmso-outline-level:1;\n\tfont-size:16.0pt;\n\tfont-family:\"Calibri Light\",sans-serif;\n\tmso-ascii-font-family:\"Calibri 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Roman\";\n\tmso-bidi-theme-font:major-bidi;\n\tcolor:#2F5496;\n\tmso-themecolor:accent1;\n\tmso-themeshade:191;}.MsoChpDefault\n\t{mso-style-type:export-only;\n\tmso-default-props:yes;\n\tfont-family:\"Calibri\",sans-serif;\n\tmso-ascii-font-family:Calibri;\n\tmso-ascii-theme-font:minor-latin;\n\tmso-fareast-font-family:Calibri;\n\tmso-fareast-theme-font:minor-latin;\n\tmso-hansi-font-family:Calibri;\n\tmso-hansi-theme-font:minor-latin;\n\tmso-bidi-font-family:\"Times New Roman\";\n\tmso-bidi-theme-font:minor-bidi;\n\tmso-fareast-language:EN-US;}div.WordSection1\n\t{page:WordSection1;}<\/style>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-071e74f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"071e74f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8c43dc4\" data-id=\"8c43dc4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aa0c527 elementor-widget elementor-widget-spacer\" data-id=\"aa0c527\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-789777a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"789777a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dd93843\" data-id=\"dd93843\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b1d0d5c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b1d0d5c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7e963bc\" data-id=\"7e963bc\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-40909d1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"40909d1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3a01f62\" data-id=\"3a01f62\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Repr\u00e9senter et caract\u00e9riser les droites du plan Introduction &nbsp; En g\u00e9om\u00e9trie analytique, les droites du plan cart\u00e9sien sont souvent d\u00e9finies par des \u00e9quations et peuvent \u00eatre caract\u00e9ris\u00e9es par plusieurs propri\u00e9t\u00e9s, dont leur vecteur directeur, leur \u00e9quation et leur pente. Ces concepts sont fondamentaux pour comprendre et travailler avec des droites dans un contexte math\u00e9matique. &nbsp; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_canvas","format":"standard","meta":{"footnotes":""},"categories":[25,26,5],"tags":[],"_links":{"self":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1930"}],"collection":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/comments?post=1930"}],"version-history":[{"count":11,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1930\/revisions"}],"predecessor-version":[{"id":2006,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/posts\/1930\/revisions\/2006"}],"wp:attachment":[{"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/media?parent=1930"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/categories?post=1930"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.maxdecours.com\/maxblog\/wp-json\/wp\/v2\/tags?post=1930"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}