{"id":3030,"date":"2020-06-09T08:17:09","date_gmt":"2020-06-09T06:17:09","guid":{"rendered":"http:\/\/jhmaths.fr\/?page_id=3030"},"modified":"2020-06-11T09:01:53","modified_gmt":"2020-06-11T07:01:53","slug":"equations-de-droites","status":"publish","type":"page","link":"https:\/\/jhmaths.fr\/index.php\/seconde\/equations-de-droites\/","title":{"rendered":"\u00c9quations de droites"},"content":{"rendered":"<p>[vc_row][vc_column][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<h1 style=\"text-align: center;\">\u00c9quation cart\u00e9sienne et vecteur directeur<\/h1>\n<p>[\/vc_column_text][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<span class=\"proprieteseconde\">Une droite dans un rep\u00e8re a pour \u00e9quation cart\u00e9sienne \\(ax+by+c=0\\)<\/span><\/p>\n<p><span class=\"proprieteseconde\">Le vecteur \\(\\overrightarrow{u}(-b;a)\\) est un vecteur directeur de la droite<\/span><\/p>\n<p><span class=\"proprieteseconde\">Si \\(A,B,M\\) sont trois points de la droite alors \\(det(\\overrightarrow{AM};\\overrightarrow{AB})=0\\)<\/span><\/p>\n<p><span class=\"proprieteseconde\">Si \\(a = 0\\) la droite est horizontale (\\(y=-\\frac{c}{b}\\) )<\/span><\/p>\n<p><span class=\"proprieteseconde\">Si \\(b=0\\) la droite est verticale (\\(x=-\\frac{c}{a}\\) )<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3045 size-large\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/06\/vecteurs-directeurs-1024x590.png\" alt=\"\" width=\"945\" height=\"544\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/06\/vecteurs-directeurs-1024x590.png 1024w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/06\/vecteurs-directeurs-300x173.png 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/06\/vecteurs-directeurs-768x443.png 768w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/06\/vecteurs-directeurs-1116x643.png 1116w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/06\/vecteurs-directeurs-806x465.png 806w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/06\/vecteurs-directeurs-558x322.png 558w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/06\/vecteurs-directeurs-655x378.png 655w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/06\/vecteurs-directeurs-820x473.png 820w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/06\/vecteurs-directeurs.png 1214w\" sizes=\"auto, (max-width: 945px) 100vw, 945px\" \/>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<h1 style=\"text-align: center;\">\u00c9quation r\u00e9duite et coefficient directeur<\/h1>\n<p>[\/vc_column_text][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<span class=\"proprieteseconde\">Une droite non verticale dans un rep\u00e8re a pour \u00e9quation r\u00e9duite \\(y=mx+p\\). C&rsquo;est l&rsquo;\u00e9quation d&rsquo;une fonction affine.<\/span><\/p>\n<p><span class=\"proprieteseconde\">Le nombre \\(m\\) est le coefficient directeur de la droite.<\/span><\/p>\n<p><span class=\"proprieteseconde\">Le nombre \\(p\\) est l&rsquo;ordonn\u00e9e \u00e0 l&rsquo;origine de la droite.<\/span>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<span class=\"proprieteseconde\">Lien entre les deux \u00e9quations :<\/span><\/p>\n<p><span class=\"proprieteseconde\">Si \\( b \\neq 0\\), on a \\(\\displaystyle y=-\\frac{a}{b}x+(-\\frac{c}{b})\\)<\/span><\/p>\n<p><span class=\"proprieteseconde\">Donc \\(\\displaystyle\u00a0 m=-\\frac{a}{b}\\)<br \/>\net \\(\\displaystyle p=-\\frac{c}{b}\\)<\/span>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h2>Quizz<\/h2>\n<p><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-71\" class=\"h5p-iframe\" data-content-id=\"71\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"2nde \u00e9quations de droites - \u00e9quation cart\u00e9sienne et r\u00e9duite\"><\/iframe><\/div>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h1 style=\"text-align: center;\">Droites parall\u00e8les ou s\u00e9cantes<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<span class=\"proprieteseconde\">Deux droites d&rsquo;\u00e9quations \\(ax+by+c=0\\) et \\(a&rsquo;x+b&rsquo;y+c&rsquo;=0\\) sont s\u00e9cantes lorsque \\(ab&rsquo;-a&rsquo;b \\neq 0\\).<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span class=\"proprieteseconde\">Dans ce cas pour trouver le point d&rsquo;intersection on r\u00e9sout le syst\u00e8me form\u00e9 par les deux \u00e9quations.<\/span>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][vc_column_text]<\/p>\n<h3>Quizz<\/h3>\n<p><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-72\" class=\"h5p-iframe\" data-content-id=\"72\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"2nde \u00e9quations de droites - positions relatives\"><\/iframe><\/div>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h1 style=\"text-align: center;\">D\u00e9monstration<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]<span class=\"proprieteseconde\">Une \u00e9quation de droite est de la forme ax + by +c = 0<\/span>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<div style=\"text-align: center;\"><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/GVDUrdsRUdA\" width=\"320\" height=\"180\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/div>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h2>Synth\u00e8se :<\/h2>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_single_image source=\u00a0\u00bbexternal_link\u00a0\u00bb onclick=\u00a0\u00bbimg_link_large\u00a0\u00bb img_link_target=\u00a0\u00bb_blank\u00a0\u00bb custom_src=\u00a0\u00bbhttps:\/\/docs.google.com\/drawings\/d\/e\/2PACX-1vSv9SMJbZbBteQ26xBAAAIHSDSJ3gVXOApRLE7RX_fhv0Ec6DbiKNMiq6g4R7hyGuokvz9cVldPVYm8\/pub?w=960&amp;h=720&Prime;][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text] \u00c9quation cart\u00e9sienne et vecteur directeur [\/vc_column_text][vc_column_text el_class=\u00a0\u00bbproprieteseconde propriete\u00a0\u00bb]Une droite dans un rep\u00e8re a pour \u00e9quation cart\u00e9sienne \\(ax+by+c=0\\) Le vecteur \\(\\overrightarrow{u}(-b;a)\\) est un vecteur directeur de la droite Si \\(A,B,M\\) sont trois points de la droite alors \\(det(\\overrightarrow{AM};\\overrightarrow{AB})=0\\) Si \\(a = 0\\) la droite est horizontale (\\(y=-\\frac{c}{b}\\) ) Si \\(b=0\\) la droite est [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2085,"menu_order":5,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"folder":[],"class_list":["post-3030","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3030","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/comments?post=3030"}],"version-history":[{"count":9,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3030\/revisions"}],"predecessor-version":[{"id":3046,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3030\/revisions\/3046"}],"up":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2085"}],"wp:attachment":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/media?parent=3030"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/folder?post=3030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}