{"id":39046,"date":"2024-06-24T15:48:00","date_gmt":"2024-06-24T13:48:00","guid":{"rendered":"https:\/\/www.swisslearn.org\/?p=39046"},"modified":"2024-08-03T11:05:47","modified_gmt":"2024-08-03T09:05:47","slug":"points-sur-un-repere-3d-2","status":"publish","type":"post","link":"https:\/\/www.swisslearn.org\/?p=39046","title":{"rendered":"Points sur un rep\u00e8re 3D"},"content":{"rendered":"\n<p>En g\u00e9om\u00e9trie plane un point est donn\u00e9 par ses deux coordonn\u00e9es :\u00a0 son abscisse <em>x<\/em> et son ordonn\u00e9e <em>y<\/em>. Par exemple A(2; 3).\u00a0<\/p>\n<p>Dans l&rsquo;espace, sur un <a href=\"https:\/\/www.swisslearn.org\/?p=38786\">rep\u00e8re en trois dimensions<\/a>, il faut une coordonn\u00e9e de plus :\u00a0 la cote <em>z<\/em>. Par exemple A(2; 3; 5).<\/p>\n<p>La difficult\u00e9 de la g\u00e9om\u00e9trie de l&rsquo;espace consiste \u00e0 projeter sur une surface \u00e0 deux dimensions (votre feuille ou l&rsquo;\u00e9cran de l&rsquo;ordinateur) une r\u00e9alit\u00e9 en trois dimensions.<\/p>\n<p>Les activit\u00e9s ci-dessous vous permettent de mieux visualiser les repr\u00e9sentations des points dans un rep\u00e8re en trois dimensions.<\/p>\n<p><strong>Activit\u00e9: <\/strong>Modifiez les coordonn\u00e9es du point A pour le visualiser en trois dimensions.<\/p>\n<p><iframe loading=\"lazy\" style=\"border: 0px;\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/b64jdy8c\/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\"><\/iframe><\/p>\n<p><strong>Exemples<\/strong><\/p>\n<table class=\" alignleft\" style=\"width: 300px; border-collapse: collapse; border-style: solid;\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.swisslearn.org\/?p=39033\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39049\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/Points-sur-repere-3D-01.png\" alt=\"\" width=\"270\" height=\"250\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.swisslearn.org\/?p=39033\">Exemple 1: point avec <br \/>trois coordonn\u00e9es positives<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\" alignleft\" style=\"width: 300px; border-collapse: collapse; border-style: solid;\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.swisslearn.org\/?p=39279\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39286\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/Points-sur-repere-3D-02-3d.png\" alt=\"\" width=\"317\" height=\"270\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.swisslearn.org\/?p=39279\">Exemple 2: point avec <br \/>abscisse <em>x<\/em> n\u00e9gatif<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\" alignleft\" style=\"width: 300px; border-collapse: collapse; border-style: solid;\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.swisslearn.org\/?p=39294\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39298\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/Points-sur-repere-3D-exemple-3-sur-sol.png\" alt=\"\" width=\"670\" height=\"600\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.swisslearn.org\/?p=39294\">Exemple 3: point sur le sol <br \/>(la cote <em>z<\/em> = 0)<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\" alignleft\" style=\"width: 300px; border-collapse: collapse; border-style: solid;\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.swisslearn.org\/?p=39304\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39307\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/Points-sur-repere-3D-exemple-4-sur-mur.png\" alt=\"\" width=\"302\" height=\"270\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.swisslearn.org\/?p=39304\">Exemple 4: point sur le mur <br \/>(l&rsquo;abscisse <em>x<\/em> = 0)<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\" alignleft\" style=\"width: 300px; border-collapse: collapse; border-style: solid;\">\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39321\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/Points-sur-repere-3D-exemple-5-sur-paroi.png\" alt=\"\" width=\"302\" height=\"270\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.swisslearn.org\/?p=39317\">Exemple 5: point sue la paroi <\/a><br \/><a href=\"https:\/\/www.swisslearn.org\/?p=39317\">(l&rsquo;ordonn\u00e9e <em>y<\/em> = 0)<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\" alignleft\" style=\"width: 300px; border-collapse: collapse; border-style: solid;\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.swisslearn.org\/?p=39324\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39327\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/Points-sur-repere-3D-exemple-6-sur-Ox.png\" alt=\"\" width=\"302\" height=\"270\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.swisslearn.org\/?p=39324\">Exemple 6: points sur l&rsquo;axe <em>Ox<\/em> (ordonn\u00e9e <em>y<\/em> et cote <em>z<\/em> = 0)<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\" alignleft\" style=\"width: 300px; border-collapse: collapse; border-style: solid;\">\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39334\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/Points-sur-repere-3D-exemple-7-sur-Oy.png\" alt=\"\" width=\"302\" height=\"270\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.swisslearn.org\/?p=39329\">Exemple 7: points sur l&rsquo;axe <em>Oy<\/em><\/a><br \/><a href=\"https:\/\/www.swisslearn.org\/?p=39329\">(abscisse <em>x<\/em> et cote <em>z<\/em> = 0)<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\" alignleft\" style=\"width: 300px; border-collapse: collapse; border-style: solid;\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.swisslearn.org\/?p=39336\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-39341\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/Points-sur-repere-3D-exemple-8-sur-Oz.png\" alt=\"\" width=\"1870\" height=\"1674\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.swisslearn.org\/?p=39336\">Exemple 8: point sur l&rsquo;axe <em>Oz<\/em><\/a><br \/><a href=\"https:\/\/www.swisslearn.org\/?p=39336\">(abscisse <em>x<\/em> et ordonn\u00e9e <em>y<\/em> = 0)<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\" alignleft\" style=\"width: 300px; border-collapse: collapse; border-style: solid;\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.swisslearn.org\/?p=39042\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39050\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/Points-sur-repere-3D-02-projections.png\" alt=\"\" width=\"298\" height=\"270\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.swisslearn.org\/?p=39042\">Exemple 9: points avec projections superpos\u00e9e<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>En g\u00e9om\u00e9trie plane un point est donn\u00e9 par ses deux coordonn\u00e9es :\u00a0 son abscisse x et son ordonn\u00e9e y. Par exemple A(2; 3).\u00a0 Dans l&rsquo;espace, sur un rep\u00e8re en trois dimensions, il faut une coordonn\u00e9e de plus :\u00a0 la cote z. Par exemple A(2; 3; 5). La difficult\u00e9 de la g\u00e9om\u00e9trie de l&rsquo;espace consiste \u00e0 [&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":[36,38,10,58],"tags":[],"class_list":["post-39046","post","type-post","status-publish","format-standard","hentry","category-astuce-du-jour","category-cours","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=36\" rel=\"category\">Astuce du jour<\/a> <a href=\"https:\/\/www.swisslearn.org\/?cat=38\" rel=\"category\">Cours<\/a> <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":"En g\u00e9om\u00e9trie plane un point est donn\u00e9 par ses deux coordonn\u00e9es :\u00a0 son abscisse x et son ordonn\u00e9e y. Par exemple A(2; 3).\u00a0 Dans l&rsquo;espace, sur un rep\u00e8re en trois dimensions, il faut une coordonn\u00e9e de plus :\u00a0 la cote z. Par exemple A(2; 3; 5). La difficult\u00e9 de la g\u00e9om\u00e9trie de l&rsquo;espace consiste \u00e0\u2026","_links":{"self":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/39046"}],"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=39046"}],"version-history":[{"count":33,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/39046\/revisions"}],"predecessor-version":[{"id":39365,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/39046\/revisions\/39365"}],"wp:attachment":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=39046"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=39046"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=39046"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}