{"id":25294,"date":"2023-04-21T09:52:22","date_gmt":"2023-04-21T08:52:22","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25294"},"modified":"2023-05-05T15:02:59","modified_gmt":"2023-05-05T14:02:59","slug":"cinco-retas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25294","title":{"rendered":"Cinco retas"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25294' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25294' class='GTTabs_curr'><a  id=\"25294_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25294' ><a  id=\"25294_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_25294'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Na figura:<br \/>\u2013 as retas <em>r<\/em> e <em>s<\/em> s\u00e3o paralelas;<br \/>\u2013 as retas <em>p<\/em> e <em>q<\/em> s\u00e3o paralelas;<br \/>\u2013 a reta <em>t<\/em> \u00e9 paralela ao eixo das abcissas.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25295\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25295\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12.png\" data-orig-size=\"273,273\" 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_Pag177-12\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12.png\" class=\"aligncenter wp-image-25295 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12.png\" alt=\"\" width=\"273\" height=\"273\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12.png 273w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12-80x80.png 80w\" sizes=\"auto, (max-width: 273px) 100vw, 273px\" \/><\/a><\/p>\n<p>Escreve as equa\u00e7\u00f5es das cinco retas representadas na figura.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25294' onClick='GTTabs_show(1,25294)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25294'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Na figura:<br \/>\u2013 as retas <em>r<\/em> e <em>s<\/em> s\u00e3o paralelas;<br \/>\u2013 as retas <em>p<\/em> e <em>q<\/em> s\u00e3o paralelas;<br \/>\u2013 a reta <em>t<\/em> \u00e9 paralela ao eixo das abcissas.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25295\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25295\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12.png\" data-orig-size=\"273,273\" 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_Pag177-12\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12.png\" class=\"aligncenter wp-image-25295 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12.png\" alt=\"\" width=\"273\" height=\"273\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12.png 273w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12-80x80.png 80w\" sizes=\"auto, (max-width: 273px) 100vw, 273px\" \/><\/a><\/p>\n<p>\u00a0<\/p>\n<p>Sejam \\(O\\left( {0,0} \\right)\\), \\(A\\left( {6,3} \\right)\\), \\(B,\\left( {1, &#8211; 2} \\right)\\), \\(C\\left( {0, &#8211; 2} \\right)\\), \\(D\\left( {0,3} \\right)\\) e \\(F\\left( {0,4} \\right)\\) pontos pertencentes \u00e0s retas consideradas, conforme sugere a figura.<\/p>\n<p>Comecemos por determinar os declives das retas <em>r<\/em> e <em>p<\/em>, tendo em considera\u00e7\u00e3o que os pontos A e O pertencem \u00e0 reta <em>r<\/em> e que os pontos C e O pertencem \u00e0 reta <em>p<\/em>:<\/p>\n<ul style=\"list-style-type: square;\">\n<li>\\({a_r} = \\frac{{3 &#8211; 0}}{{6 &#8211; 0}} = \\frac{1}{2}\\)<\/li>\n<li>\\({a_p} = \\frac{{ &#8211; 2 &#8211; 0}}{{1 &#8211; 0}} = &#8211; 2\\)<\/li>\n<\/ul>\n<p>Assim, podemos escrever as equa\u00e7\u00f5es das retas <em>r<\/em> e <em>p<\/em>, respetivamente: \\(y = \\frac{1}{2}x\\) e \\(y = &#8211; 2x\\).<\/p>\n<p>Tendo em considera\u00e7\u00e3o as ordenadas na origem das retas <em>s<\/em> e <em>q<\/em> e sabendo que retas paralelas possuem igual declive, podemos agora escrever as equa\u00e7\u00f5es destas duas retas, respetivamente: \\(y = \\frac{1}{2}x &#8211; 2\\) e \\(y = &#8211; 2x + 3\\).<\/p>\n<p>Finalmente, a equa\u00e7\u00e3o da reta <em>t<\/em>, de declive nulo: \\(y = 4\\).<\/p>\n<p>Em s\u00edntese, temos:<\/p>\n<ul style=\"list-style-type: disc;\">\n<li>\\(p:y = &#8211; 2x\\)<\/li>\n<li>\\(q:y = &#8211; 2x + 3\\)<\/li>\n<li>\\(r:y = \\frac{1}{2}x\\)<\/li>\n<li>\\(s:y = \\frac{1}{2}x &#8211; 2\\)<\/li>\n<li>\\(t:y = 4\\)<\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25294' onClick='GTTabs_show(0,25294)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura:\u2013 as retas r e s s\u00e3o paralelas;\u2013 as retas p e q s\u00e3o paralelas;\u2013 a reta t \u00e9 paralela ao eixo das abcissas. Escreve as equa\u00e7\u00f5es das cinco retas&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":25296,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,709],"tags":[424,345,344,712],"series":[],"class_list":["post-25294","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-aos-eixos-coordenados"],"views":49,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-12_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25294","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=25294"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25294\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25296"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25294"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25294"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25294"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25294"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}