{"id":13481,"date":"2018-02-05T18:18:33","date_gmt":"2018-02-05T18:18:33","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13481"},"modified":"2022-01-16T14:38:53","modified_gmt":"2022-01-16T14:38:53","slug":"qual-e-a-distancia-do-ponto-p-ao-plano-alpha","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13481","title":{"rendered":"Qual \u00e9 a dist\u00e2ncia do ponto P ao plano \\(\\alpha \\)"},"content":{"rendered":"<p><ul id='GTTabs_ul_13481' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13481' class='GTTabs_curr'><a  id=\"13481_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13481' ><a  id=\"13481_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_13481'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13482\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13482\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2.png\" data-orig-size=\"205,150\" 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=\"Plano\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2.png\" class=\"alignright size-full wp-image-13482\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2.png\" alt=\"\" width=\"205\" height=\"150\" \/><\/a>O ponto P&#8217; \u00e9 a proje\u00e7\u00e3o ortogonal do ponto P no plano\u00a0\\(\\alpha \\).<br \/>\nA \u00e9 um ponto do plano\u00a0\\(\\alpha \\), distinto de P&#8217;.<\/p>\n<p>A dist\u00e2ncia do ponto P ao ponto A \u00e9 50 cm e a dist\u00e2ncia do ponto P&#8217; ao ponto A \u00e9 14 cm.<\/p>\n<p>Qual \u00e9 a dist\u00e2ncia do ponto P ao plano\u00a0\\(\\alpha \\)?<br \/>\nExplica a tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13481' onClick='GTTabs_show(1,13481)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13481'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13482\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13482\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2.png\" data-orig-size=\"205,150\" 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=\"Plano\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2.png\" class=\"alignright size-full wp-image-13482\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2.png\" alt=\"\" width=\"205\" height=\"150\" \/><\/a>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [APP&#8217;], vem:<\/p>\n<p>\\[\\overline {PP&#8217;} = \\sqrt {{{\\overline {AP} }^2} &#8211; {{\\overline {AP&#8217;} }^2}} = \\sqrt {{{50}^2} &#8211; {{14}^2}} = \\sqrt {2500 &#8211; 196} = \\sqrt {2304} = 48\\]<\/p>\n<p>Portanto,\u00a0a dist\u00e2ncia do ponto P ao plano\u00a0\\(\\alpha \\) \u00e9 48 cm.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13481' onClick='GTTabs_show(0,13481)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O ponto P&#8217; \u00e9 a proje\u00e7\u00e3o ortogonal do ponto P no plano\u00a0\\(\\alpha \\). A \u00e9 um ponto do plano\u00a0\\(\\alpha \\), distinto de P&#8217;. A dist\u00e2ncia do ponto P ao ponto A&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20366,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,467],"series":[],"class_list":["post-13481","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-distancias-areas-e-volumes-de-solidos","tag-9-o-ano","tag-distancia"],"views":1458,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13481","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=13481"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13481\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20366"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13481"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13481"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13481"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13481"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}