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{"id":23854,"date":"2022-12-24T18:25:03","date_gmt":"2022-12-24T18:25:03","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23854"},"modified":"2023-01-09T00:07:13","modified_gmt":"2023-01-09T00:07:13","slug":"observa-os-pontos-marcados-no-referencial","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23854","title":{"rendered":"Observa os pontos marcados no referencial"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23854' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23854' class='GTTabs_curr'><a  id=\"23854_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23854' ><a  id=\"23854_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_23854'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23857\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23857\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5.png\" data-orig-size=\"468,380\" 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_Pag088-5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5.png\" class=\"wp-image-23857 alignright\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5-300x244.png\" alt=\"\" width=\"300\" height=\"244\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5-300x244.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5.png 468w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Observa os pontos marcados no referencial da figura.<\/p>\n<ol>\n<li>Indica as coordenadas dos pontos A, B e C.<\/li>\n<li>Marca o ponto N tal que \\(\\overrightarrow {DC} = \\overrightarrow {AN} \\).<br \/>Quais s\u00e3o as suas coordenadas?<\/li>\n<li>D \u00e9 a imagem do ponto M pela transla\u00e7\u00e3o de vetor \\({\\vec v}\\). Quais s\u00e3o as coordenadas de M?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23854' onClick='GTTabs_show(1,23854)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23854'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5-Resolucao.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23860\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23860\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5-Resolucao.png\" data-orig-size=\"657,422\" 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_Pag088-5-Resolucao\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5-Resolucao.png\" class=\"alignright wp-image-23860\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5-Resolucao-300x193.png\" alt=\"\" width=\"420\" height=\"270\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5-Resolucao-300x193.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5-Resolucao.png 657w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a>Consideremos os pontos marcados a cor preta no referencial da figura .<\/p>\n<ol>\n<li>As coordenadas dos pontos A, B e C s\u00e3o as seguintes: \\(A\\left( {2,3} \\right)\\), \\(B\\left( {1, &#8211; 2} \\right)\\) e \\(C\\left( { &#8211; 3, &#8211; 1} \\right)\\).<\/li>\n<li>Est\u00e1 marcado o ponto N tal que \\(\\overrightarrow {DC} = \\overrightarrow {AN} \\).<br \/>As suas coordenadas s\u00e3o \\(N\\left( {0, &#8211; 1} \\right)\\).<\/li>\n<li>Seja D a imagem do ponto M pela transla\u00e7\u00e3o de vetor \\({\\vec v}\\).<br \/>Ent\u00e3o, \\(M\\left( { &#8211; 5,1} \\right)\\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23854' onClick='GTTabs_show(0,23854)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa os pontos marcados no referencial da figura. Indica as coordenadas dos pontos A, B e C. Marca o ponto N tal que \\(\\overrightarrow {DC} = \\overrightarrow {AN} \\).Quais s\u00e3o as&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23858,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,685],"tags":[424,67,381,688],"series":[],"class_list":["post-23854","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-isometrias","tag-8-o-ano","tag-geometria","tag-translacao","tag-vetores"],"views":175,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag088-5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23854","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=23854"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23854\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23858"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23854"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23854"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23854"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23854"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}