{"id":24328,"date":"2023-01-08T21:53:48","date_gmt":"2023-01-08T21:53:48","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24328"},"modified":"2023-01-17T23:44:15","modified_gmt":"2023-01-17T23:44:15","slug":"pontos-marcados-num-referencial","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24328","title":{"rendered":"Pontos marcados num referencial"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24328' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24328' class='GTTabs_curr'><a  id=\"24328_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24328' ><a  id=\"24328_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_24328'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24329\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24329\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5.png\" data-orig-size=\"261,322\" 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_Pag115-5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5.png\" class=\"alignright wp-image-24329 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5.png\" alt=\"\" width=\"261\" height=\"322\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5.png 261w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5-243x300.png 243w\" sizes=\"auto, (max-width: 261px) 100vw, 261px\" \/><\/a>Observa os pontos marcados no referencial da figura.<\/p>\n<ol>\n<li>Quais s\u00e3o as coordenadas do ponto D, imagem do ponto C pela transla\u00e7\u00e3o de vetor \\(\\overrightarrow {BA} \\)?<\/li>\n<li>Justifica que o quadril\u00e1tero [ABCD] \u00e9 um paralelogramo.<\/li>\n<li>Determina o comprimento do segmento de reta [BC].<\/li>\n<li>O ponto E \u00e9 a imagem do ponto A pela simetria central de centro C.<br \/>Indica as coordenadas de ponto E.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24328' onClick='GTTabs_show(1,24328)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24328'>\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\/01\/8_Pag115-5_SOL.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24332\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24332\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5_SOL.png\" data-orig-size=\"880,938\" 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_Pag115-5_SOL\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5_SOL.png\" class=\"alignright wp-image-24332\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5_SOL-281x300.png\" alt=\"\" width=\"420\" height=\"448\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5_SOL-281x300.png 281w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5_SOL-768x819.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5_SOL.png 880w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a>Observa os pontos marcados no referencial da figura.<\/p>\n<ol>\n<li>O ponto D, imagem do ponto C pela transla\u00e7\u00e3o de vetor \\(\\overrightarrow {BA} \\), tem coordenadas \\(\\left( {2,2} \\right)\\).<br \/><br \/><\/li>\n<li>Os segmentos orientados [B, A] e [C, D] s\u00e3o equipolentes, bem como tamb\u00e9m s\u00e3o equipolentes os segmentos orientados [C, B] e [D, A]. Consequentemente, o quadril\u00e1tero [ABCD] possui os lados opostos paralelos, pelo que ser\u00e1, ent\u00e3o, um paralelogramo.<br \/><br \/><\/li>\n<li>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [BPC], temos: \\(\\overline {BC} = \\sqrt {{{\\overline {BP} }^2} + {{\\overline {CP} }^2}} = \\sqrt {{3^2} + {5^2}} = \\sqrt {34} \\).<br \/><br \/><\/li>\n<li>Como o ponto E \u00e9 a imagem do ponto A pela simetria central de centro C, ent\u00e3o C \u00e9 o ponto m\u00e9dio do segmento de reta [AE]. As coordenadas de ponto E s\u00e3o \\(\\left( { &#8211; 9,9} \\right)\\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24328' onClick='GTTabs_show(0,24328)'>&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. Quais s\u00e3o as coordenadas do ponto D, imagem do ponto C pela transla\u00e7\u00e3o de vetor \\(\\overrightarrow {BA} \\)? Justifica que o quadril\u00e1tero [ABCD]&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":24330,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,685],"tags":[424,67,166,381,688],"series":[],"class_list":["post-24328","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-simetria","tag-translacao","tag-vetores"],"views":299,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/01\/8_Pag115-5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24328","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=24328"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24328\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/24330"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24328"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}