{"id":200,"date":"2023-04-05T04:40:30","date_gmt":"2023-04-05T04:40:30","guid":{"rendered":"https:\/\/www.wagammaths.com\/?page_id=200"},"modified":"2023-04-07T13:29:19","modified_gmt":"2023-04-07T13:29:19","slug":"homothetie","status":"publish","type":"page","link":"https:\/\/www.wagammaths.com\/index.php\/3e\/homothetie\/","title":{"rendered":"Homoth\u00e9tie"},"content":{"rendered":"<p><span style=\"color: #000000;\">On consid\u00e8re un point \\(A\\) du plan et un nombre \\({k}\\ne {0}\\). On appelle homoth\u00e9tie de centre \\(A\\) et de rapport \\(k\\) la transformation du plan qui \u00e0 chaque point \\(M\\) associe le point \\(M&#8217;\\)\u00a0tel que :\u00a0<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">A, M et M&#8217; sont align\u00e9s<\/span><\/li>\n<li><span style=\"color: #000000;\">Si \\({k}\\gg {0}\\), \\(M\\) et \\(M&#8217;\\) sont du m\u00eame c\u00f4t\u00e9 du point \\(A\\), et \\(AM&#8217; = k \u00d7 AM\\)<\/span><\/li>\n<li><span style=\"color: #000000;\">Si \\({k}\\ll {0}\\), \\(M\\) et \\(M&#8217;\\) sont de part et d&#8217;autre du point \\(A\\), et \\(AM&#8217; = -k \u00d7 AM\\)<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #0000ff;\"><strong>Exemple :\u00a0<\/strong><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-208 size-full\" src=\"https:\/\/www.wagammaths.com\/wp-content\/uploads\/2023\/04\/homothetie.png\" alt=\"\" width=\"641\" height=\"466\" srcset=\"https:\/\/www.wagammaths.com\/wp-content\/uploads\/2023\/04\/homothetie.png 641w, https:\/\/www.wagammaths.com\/wp-content\/uploads\/2023\/04\/homothetie-300x218.png 300w, https:\/\/www.wagammaths.com\/wp-content\/uploads\/2023\/04\/homothetie-600x436.png 600w\" sizes=\"auto, (max-width: 641px) 100vw, 641px\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">Le triangle ABC est l&#8217;image du triangle ABC par l&#8217;homoth\u00e9tie de centre \\(O\\) et de rapport \\(k=0,5\\)<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>On consid\u00e8re un point du plan et un nombre . On appelle homoth\u00e9tie de centre et de rapport la transformation du plan qui \u00e0 chaque&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":65,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-200","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/pages\/200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=200"}],"version-history":[{"count":8,"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/pages\/200\/revisions"}],"predecessor-version":[{"id":209,"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/pages\/200\/revisions\/209"}],"up":[{"embeddable":true,"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/pages\/65"}],"wp:attachment":[{"href":"https:\/\/www.wagammaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}