{"id":25115,"date":"2023-04-15T11:51:12","date_gmt":"2023-04-15T10:51:12","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25115"},"modified":"2023-04-27T00:39:40","modified_gmt":"2023-04-26T23:39:40","slug":"mais-quatro-retas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25115","title":{"rendered":"Mais quatro retas"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25115' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25115' class='GTTabs_curr'><a  id=\"25115_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25115' ><a  id=\"25115_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_25115'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25117\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25117\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4.png\" data-orig-size=\"276,955\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag171-4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4.png\" class=\"alignright wp-image-25117\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4-87x300.png\" alt=\"\" width=\"160\" height=\"554\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4-87x300.png 87w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4.png 276w\" sizes=\"auto, (max-width: 160px) 100vw, 160px\" \/><\/a><\/p>\n<p>Observa a figura.<\/p>\n<ol>\n<li>Sabendo que uma equa\u00e7\u00e3o da reta <em>r<\/em> \u00e9 \\(y = &#8211; \\frac{3}{2}x\\) e que as retas <em>r<\/em> e AB s\u00e3o paralelas, indica uma equa\u00e7\u00e3o da reta AB.<\/li>\n<li>Escreve uma equa\u00e7\u00e3o da reta paralela a CD e que passa no ponto \\(P\\left( {0,\\,2} \\right)\\).<\/li>\n<li>As retas EF e <em>s<\/em> s\u00e3o paralelas e \\(y = 2x + 3\\) \u00e9 uma equa\u00e7\u00e3o da reta EF.<br>Escreve uma equa\u00e7\u00e3o da reta <em>s<\/em>.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25115' onClick='GTTabs_show(1,25115)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25115'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25117\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25117\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4.png\" data-orig-size=\"276,955\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag171-4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4.png\" class=\"alignright wp-image-25117\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4-87x300.png\" alt=\"\" width=\"160\" height=\"554\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4-87x300.png 87w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4.png 276w\" sizes=\"auto, (max-width: 160px) 100vw, 160px\" \/><\/a><\/p>\n<blockquote>\n<p>Observa a figura.<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote>Sabendo que uma equa\u00e7\u00e3o da reta <em>r<\/em> \u00e9 \\(y = &#8211; \\frac{3}{2}x\\) e que as retas <em>r<\/em> e AB s\u00e3o paralelas, indica uma equa\u00e7\u00e3o da reta AB.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Escreve uma equa\u00e7\u00e3o da reta paralela a CD e que passa no ponto \\(P\\left( {0,\\,2} \\right)\\).<\/blockquote>\n<\/li>\n<li>\n<blockquote>As retas EF e <em>s<\/em> s\u00e3o paralelas e \\(y = 2x + 3\\) \u00e9 uma equa\u00e7\u00e3o da reta EF.<br>Escreve uma equa\u00e7\u00e3o da reta <em>s<\/em>.<\/blockquote>\n<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<ol>\n<li>Como as retas <em>r<\/em> e AB s\u00e3o paralelas, ent\u00e3o t\u00eam igual declive. Logo, \\({a_{AB}} = {a_r} = &#8211; \\frac{3}{4}\\).<br>Como \\(A\\left( {0,\\,2} \\right)\\), ent\u00e3o a ordenada na origem da reta AB \u00e9 \\({b_{AB}} = 2\\).<br>Assim, \\(y = &#8211; \\frac{3}{4}x + 2\\) \u00e9 uma equa\u00e7\u00e3o da reta AB.<br><br><\/li>\n<li>Como as retas s\u00e3o paralelas, ent\u00e3o t\u00eam igual declive. Logo, \\(a = {a_{CD}} = \\frac{7}{2}\\).<br>Como \\(P\\left( {0,\\,2} \\right)\\), ent\u00e3o a ordenada na origem dessa reta \u00e9 \\(b = 2\\).<br>Assim, \\(y = \\frac{7}{2}x + 2\\) \u00e9 uma equa\u00e7\u00e3o da reta considerada.<br><br><\/li>\n<li>De modo an\u00e1logo, conclui-se que uma equa\u00e7\u00e3o da reta <em>s<\/em> \u00e9 \\(y = 2x\\), j\u00e1 que a ordenada na origem da reta <em>s<\/em> \u00e9 0.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25115' onClick='GTTabs_show(0,25115)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa a figura. Sabendo que uma equa\u00e7\u00e3o da reta r \u00e9 \\(y = &#8211; \\frac{3}{2}x\\) e que as retas r e AB s\u00e3o paralelas, indica uma equa\u00e7\u00e3o da reta AB. Escreve&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":25119,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,709],"tags":[424,345,344,711],"series":[],"class_list":["post-25115","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-graficos-de-funcoes-afins","tag-8-o-ano","tag-funcao-afim","tag-grafico","tag-retas-paralelas"],"views":71,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag171-4c_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25115","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=25115"}],"version-history":[{"count":1,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25115\/revisions"}],"predecessor-version":[{"id":25127,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25115\/revisions\/25127"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25119"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25115"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25115"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25115"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}