{"id":38858,"date":"2024-06-17T15:34:31","date_gmt":"2024-06-17T13:34:31","guid":{"rendered":"https:\/\/www.swisslearn.org\/?p=38858"},"modified":"2024-06-25T14:38:08","modified_gmt":"2024-06-25T12:38:08","slug":"partie-visible-dune-droite-exemple-n-7","status":"publish","type":"post","link":"https:\/\/www.swisslearn.org\/?p=38858","title":{"rendered":"Partie visible d&rsquo;une droite: exemple n\u00b0 7"},"content":{"rendered":"\n\n<p><a href=\"https:\/\/www.swisslearn.org\/?p=38803\">Exemples<\/a> n\u00b0 <a href=\"https:\/\/www.swisslearn.org\/?p=38825\">1<\/a>, <a href=\"https:\/\/www.swisslearn.org\/?p=38836\">2<\/a>, <a href=\"https:\/\/www.swisslearn.org\/?p=38840\">3<\/a>, <a href=\"https:\/\/www.swisslearn.org\/?p=38844\">4<\/a>, <a href=\"https:\/\/www.swisslearn.org\/?p=38852\">5<\/a>, <a href=\"https:\/\/www.swisslearn.org\/?p=38854\">6<\/a>, 7<iframe loading=\"lazy\" style=\"border: 0px;\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/ghxp4wtr\/width\/1200\/height\/715\/border\/888888\/rc\/true\/ai\/false\/sdz\/true\/smb\/false\/stb\/false\/stbh\/true\/ld\/false\/sri\/false\/sfsb\/true\" width=\"1600px\" height=\"715px\" scrolling=\"no\" allowfullscreen=\"allowfullscreen\" data-mce-fragment=\"1\"><br \/><\/iframe><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?d:\\left\\{\\begin{matrix}&amp;space;x=-5-5k&amp;space;\\\\&amp;space;y=4+2k&amp;space;\\\\&amp;space;z=3k&amp;space;\\end{matrix}\\right.\" alt=\"d:\\left\\{\\begin{matrix} x=-5-5k \\\\ y=4+2k \\\\ z=3k \\end{matrix}\\right.\" align=\"absmiddle\" \/><\/p>\n<p><strong>Point A, intersection avec le sol (z = 0):<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?A&amp;space;\\in&amp;space;Sol&amp;space;\\Rightarrow&amp;space;z=0\" alt=\"A \\in Sol \\Rightarrow z=0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;3k=0&amp;space;\\Rightarrow&amp;space;k=0\" alt=\"\\Rightarrow 3k=0 \\Rightarrow k=0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;x=-5-5\\cdot&amp;space;0=-5\" alt=\"\\Rightarrow x=-5-5\\cdot 0=-5\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?y=4+2\\cdot0=4\" alt=\"y=4+2\\cdot0=4\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?A(-5;&amp;space;4;&amp;space;0)\" alt=\"A(-5; 4; 0)\" align=\"absmiddle\" \/><\/p>\n<p>La droite <em>d<\/em> coupe le sol au point A. L&rsquo;abscisse x de ce point est n\u00e9gative. La droite <em>d<\/em> coupe donc le sol derri\u00e8re le mur. Le point A ne fait donc pas partie de la partie visible de la droite.<\/p>\n<p><strong>Point B, intersection avec le mur (x = 0):<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?B&amp;space;\\in&amp;space;Mur&amp;space;\\Rightarrow&amp;space;x=0\" alt=\"B \\in Mur \\Rightarrow x=0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;-5-5k=0&amp;space;\\Rightarrow&amp;space;k=-1\" alt=\"\\Rightarrow -5-5k=0 \\Rightarrow k=-1\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;y=4+2\\cdot&amp;space;(-1)=2\" alt=\"\\Rightarrow y=4+2\\cdot (-1)=2\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?z=3\\cdot&amp;space;(-1)=-3\" alt=\"z=3\\cdot (-1)=-3\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?B(0;&amp;space;2;&amp;space;-3)\" alt=\"B(0; 2; -3)\" align=\"absmiddle\" \/><\/p>\n<p><strong>Point C, intersection avec la paroi (y = 0):<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?C&amp;space;\\in&amp;space;Paroi&amp;space;\\Rightarrow&amp;space;y=0\" alt=\"C \\in Paroi \\Rightarrow y=0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;4+2k=0&amp;space;\\Rightarrow&amp;space;k=-2\" alt=\"\\Rightarrow 4+2k=0 \\Rightarrow k=-2\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;x=-5-5\\cdot&amp;space;(-2)=5\" alt=\"\\Rightarrow x=-5-5\\cdot (-2)=5\" align=\"absmiddle\" \/>\u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;z=3\\cdot&amp;space;(-2)=-6\" alt=\"\\Rightarrow z=3\\cdot (-2)=-6\" align=\"absmiddle\" \/><\/p>\n<p>La droite <em>d<\/em> coupe la paroi au point C dont la cote <em>z<\/em> est n\u00e9gative. Elle coupe donc la paroi en un point qui est sous le sol. Le point C n&rsquo;appartient donc pas \u00e0 la partie visible de cette droite.<\/p>\n<p>Les points d&rsquo;intersection de la droite <em>d<\/em> avec les trois plans du rep\u00e8re se trouvent tous en dehors de la zone de visibilit\u00e9, derri\u00e8re le mur, la parois et le sol. Cette droite n&rsquo;a donc pas de partie visible.<\/p>\n<p><!-- \/wp:tadv\/classic-paragraph --><\/p>","protected":false},"excerpt":{"rendered":"<p>Exemples n\u00b0 1, 2, 3, 4, 5, 6, 7 Point A, intersection avec le sol (z = 0): \u00a0 \u00a0 \u00a0 La droite d coupe le sol au point A. L&rsquo;abscisse x de ce point est n\u00e9gative. La droite d coupe donc le sol derri\u00e8re le mur. Le point A ne fait donc pas partie [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"off","_et_pb_old_content":"","_et_gb_content_width":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[10,58],"tags":[],"class_list":["post-38858","post","type-post","status-publish","format-standard","hentry","category-geometrie","category-geometrie-de-lespace"],"blocksy_meta":"","rttpg_featured_image_url":null,"rttpg_author":{"display_name":"Bahram Zaerpour","author_link":"https:\/\/www.swisslearn.org\/?author=1"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/www.swisslearn.org\/?cat=10\" rel=\"category\">G\u00e9om\u00e9trie<\/a> <a href=\"https:\/\/www.swisslearn.org\/?cat=58\" rel=\"category\">G\u00e9om\u00e9trie de l'espace<\/a>","rttpg_excerpt":"Exemples n\u00b0 1, 2, 3, 4, 5, 6, 7 Point A, intersection avec le sol (z = 0): \u00a0 \u00a0 \u00a0 La droite d coupe le sol au point A. L&rsquo;abscisse x de ce point est n\u00e9gative. La droite d coupe donc le sol derri\u00e8re le mur. Le point A ne fait donc pas partie\u2026","_links":{"self":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/38858"}],"collection":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=38858"}],"version-history":[{"count":8,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/38858\/revisions"}],"predecessor-version":[{"id":39086,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/38858\/revisions\/39086"}],"wp:attachment":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=38858"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=38858"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=38858"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}