{"id":26239,"date":"2023-06-05T19:37:25","date_gmt":"2023-06-05T18:37:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26239"},"modified":"2023-06-05T21:20:14","modified_gmt":"2023-06-05T20:20:14","slug":"duas-retas-representadas-num-referencial-cartesiano","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26239","title":{"rendered":"Duas retas representadas num referencial cartesiano"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26239' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26239' class='GTTabs_curr'><a  id=\"26239_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26239' ><a  id=\"26239_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_26239'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26242\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26242\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4.png\" data-orig-size=\"314,292\" 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_Pag209-4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4.png\" class=\"alignright wp-image-26242\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4-300x279.png\" alt=\"\" width=\"300\" height=\"279\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4-300x279.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4.png 314w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>Na figura, est\u00e3o representadas, num referencial cartesiano, as retas <em>r<\/em> e <em>s<\/em>.<\/p>\n<p>Sabe-se que:<\/p>\n<ul>\n<li>a reta <em>r<\/em> \u00e9 definida por \\(y = 0,6x\\);<\/li>\n<li>a reta <em>s<\/em> \u00e9 definida por \\(y = &#8211; 1,2x + 4,5\\);<\/li>\n<li>o ponto <em>A<\/em> \u00e9 o ponto de interse\u00e7\u00e3o da reta <em>s<\/em> com o eixo das abcissas;<\/li>\n<li>o ponto <em>B<\/em> \u00e9 o ponto de interse\u00e7\u00e3o da reta <em>s<\/em> com o eixo das ordenadas;<\/li>\n<li>o ponto <em>I<\/em> \u00e9 o ponto de interse\u00e7\u00e3o das retas <em>r<\/em> e <em>s<\/em>.<\/li>\n<\/ul>\n<ol>\n<li>Qual \u00e9 a ordenada do ponto <em>B<\/em>?<\/li>\n<li>Qual \u00e9 a medida do comprimento do segmento de reta [<em>OA<\/em>]?<br \/>Transcreve a letra da op\u00e7\u00e3o correta.<br \/><strong>[A]<\/strong> \\(3,5\\)\u00a0 \u00a0 \u00a0 \u00a0 <strong>[B]<\/strong> \\(3,75\\)\u00a0 \u00a0 \u00a0 \u00a0 <strong>[C]<\/strong> \\(4,5\\)\u00a0 \u00a0 \u00a0 \u00a0 <strong>[D]<\/strong> \\(4,75\\)<\/li>\n<li>Determina as coordenadas do ponto <em>I<\/em>.<br \/>Mostra como chegaste \u00e0 tua resposta.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26239' onClick='GTTabs_show(1,26239)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26239'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26242\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26242\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4.png\" data-orig-size=\"314,292\" 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_Pag209-4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4.png\" class=\"alignright wp-image-26242\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4-300x279.png\" alt=\"\" width=\"300\" height=\"279\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4-300x279.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4.png 314w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>Na figura, est\u00e3o representadas, num referencial cartesiano, as retas <em>r<\/em> e <em>s<\/em>.<\/p>\n<p>Sabe-se que:<\/p>\n<\/blockquote>\n<ul>\n<li>\n<blockquote>a reta <em>r<\/em> \u00e9 definida por \\(y = 0,6x\\);<\/blockquote>\n<\/li>\n<li>\n<blockquote>a reta <em>s<\/em> \u00e9 definida por \\(y = &#8211; 1,2x + 4,5\\);<\/blockquote>\n<\/li>\n<li>\n<blockquote>o ponto <em>A<\/em> \u00e9 o ponto de interse\u00e7\u00e3o da reta <em>s<\/em> com o eixo das abcissas;<\/blockquote>\n<\/li>\n<li>\n<blockquote>o ponto <em>B<\/em> \u00e9 o ponto de interse\u00e7\u00e3o da reta <em>s<\/em> com o eixo das ordenadas;<\/blockquote>\n<\/li>\n<li>\n<blockquote>o ponto <em>I<\/em> \u00e9 o ponto de interse\u00e7\u00e3o das retas <em>r<\/em> e <em>s<\/em>.<\/blockquote>\n<\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<ol>\n<li>O ponto <em>B<\/em> \u00e9 a interse\u00e7\u00e3o da reta <em>s<\/em> com o eixo <em>Oy<\/em>.<br \/>A ordenada do ponto <em>B<\/em> \u00e9 \\(4,5\\), pois \u00e9 a ordenada na origem da reta <em>s<\/em>.<br \/><br \/><\/li>\n<li>O ponto <em>A<\/em> \u00e9 a interse\u00e7\u00e3o da reta <em>s<\/em> com o eixo <em>Ox<\/em>.<br \/>Esse ponto tem ordenada nula.<br \/>Logo, a sua abcissa \u00e9 a solu\u00e7\u00e3o da equa\u00e7\u00e3o \\(\\begin{array}{*{20}{c}}{ &#8211; 1,2x + 4,5 = 0}&amp; \\Leftrightarrow &amp;{x = \\frac{{4,5}}{{1,2}}}&amp; \\Leftrightarrow &amp;{x = 3,75}\\end{array}\\).<br \/>Assim, a medida do comprimento do segmento de reta [<em>OA<\/em>] \u00e9 \\({3,75}\\).<br \/>Portanto, a op\u00e7\u00e3o correta \u00e9 <strong>[B]<\/strong> \\(3,75\\).<br \/><br \/><\/li>\n<li>As coordenadas do ponto <em>I<\/em> s\u00e3o \\(\\left( {2,5;1,5} \\right)\\).<br \/>\\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{y = 0,6x}\\\\{y = &#8211; 1,2x + 4,5}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = 0,6x}\\\\{0,6x = &#8211; 1,2x + 4,5}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = 0,6x}\\\\{1,8x = 4,5}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = 2,5}\\\\{y = 1,5}\\end{array}} \\right.}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26239' onClick='GTTabs_show(0,26239)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, est\u00e3o representadas, num referencial cartesiano, as retas r e s. Sabe-se que: a reta r \u00e9 definida por \\(y = 0,6x\\); a reta s \u00e9 definida por \\(y =&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":26243,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,345,239],"series":[],"class_list":["post-26239","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-literais-e-sistemas","tag-8-o-ano","tag-funcao-afim","tag-sistema-de-equacoes"],"views":142,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag209-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26239","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=26239"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26239\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/26243"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26239"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26239"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26239"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}