{"id":23954,"date":"2022-12-28T23:24:24","date_gmt":"2022-12-28T23:24:24","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23954"},"modified":"2023-01-17T23:26:47","modified_gmt":"2023-01-17T23:26:47","slug":"os-mosaicos-e-os-vetores","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23954","title":{"rendered":"Os mosaicos e os vetores"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23954' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23954' class='GTTabs_curr'><a  id=\"23954_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23954' ><a  id=\"23954_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_23954'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23957\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23957\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10.png\" data-orig-size=\"485,510\" 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_Pag098-T10\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10.png\" class=\"wp-image-23957 alignright\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10-285x300.png\" alt=\"\" width=\"360\" height=\"379\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10-285x300.png 285w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10.png 485w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>Observa os mosaicos e os vetores \\({\\vec a}\\) e \\({\\vec b}\\).<\/p>\n<ol>\n<li>Relaciona com \\({\\vec a}\\) e \\({\\vec b}\\) o vetor que define a transla\u00e7\u00e3o que transforma:<br \/>a) a figura A na F;<br \/>b) a figura A na E;<br \/>c) a figura E na C.<\/li>\n<li>Indica o centro e a amplitude de rota\u00e7\u00f5es que transformem:<br \/>a) a figura A na E;<br \/>b) a figura B na C.<\/li>\n<li>Qual \u00e9 o transformado pela reflex\u00e3o axial de eixo O&#8217;O&#8221;:<br \/>a) da figura D?<br \/>b) da figura C?<\/li>\n<li>Que tipo de isometria transforma a figura E na figura B?<\/li>\n<li><strong>Verdadeiro ou Falso?<\/strong><br \/>Em todas as transforma\u00e7\u00f5es geom\u00e9tricas atr\u00e1s indicadas,<br \/>a) um segmento de reta \u00e9 transformado noutro congruente;<br \/>b) um \u00e2ngulo \u00e9 transformado noutro de amplitude diferente;<br \/>c) uma semirreta \u00e9 transformada noutra semirreta com a mesma dire\u00e7\u00e3o e sentido;<br \/>d) cada figura \u00e9 transformada noutra congruente;<br \/>e) h\u00e1 pontos que se mant\u00eam fixos.<br \/>f) um segmento de reta \u00e9 transformado noutro que lhe \u00e9 paralelo.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23954' onClick='GTTabs_show(1,23954)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23954'>\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_Pag098-T10.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23957\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23957\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10.png\" data-orig-size=\"485,510\" 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_Pag098-T10\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10.png\" class=\"wp-image-23957 alignright\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10-285x300.png\" alt=\"\" width=\"360\" height=\"379\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10-285x300.png 285w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10.png 485w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>Observa os mosaicos e os vetores \\({\\vec a}\\) e \\({\\vec b}\\).<\/p>\n<ol>\n<li>Relaciona com \\({\\vec a}\\) e \\({\\vec b}\\) o vetor que define a transla\u00e7\u00e3o que transforma:<br \/>a) a figura A na F;\u00a0 \u00a0 <span style=\"color: #0000ff;\">R: \\({T_{\\vec b}}\\left( A \\right) = F\\).<\/span><br \/>b) a figura A na E;\u00a0 \u00a0 <span style=\"color: #0000ff;\">R: \\({T_{ &#8211; \\vec b}}\\left( A \\right) = E\\).<\/span><br \/>c) a figura E na C.\u00a0 \u00a0 \u00a0<span style=\"color: #0000ff;\">R: \\({T_{\\vec a + \\vec b}}\\left( E \\right) = C\\).<\/span><\/li>\n<li>Indica o centro e a amplitude de rota\u00e7\u00f5es que transformem:<br \/>a) a figura A na E; <span style=\"color: #0000ff;\">R: \\({R_{O,90^\\circ }}\\left( A \\right) = E\\) e \\({R_{O&#8217;,180^\\circ }}\\left( A \\right) = E\\).<\/span><br \/>b) a figura B na C. <span style=\"color: #0000ff;\">R: \\({R_{{O^{&#8221;}}, &#8211; 90^\\circ }}\\left( B \\right) = C\\).<\/span><\/li>\n<li>Qual \u00e9 o transformado pela reflex\u00e3o axial de eixo O&#8217;O&#8221;:<br \/>a) da figura D?\u00a0 \u00a0 <span style=\"color: #0000ff;\">R: \u00c9 a figura E.<\/span><br \/>b) da figura C?\u00a0 \u00a0 <span style=\"color: #0000ff;\">R: \u00c9 a figura B.<\/span><\/li>\n<li>Que tipo de isometria transforma a figura E na figura B?<br \/><span style=\"color: #0000ff;\">Reflex\u00e3o deslizante de eixo O&#8217;O&#8221; e vetor \\(\\vec a + \\vec b\\), por exemplo.<\/span><\/li>\n<li><strong>Verdadeiro ou Falso?<\/strong><br \/>Em todas as transforma\u00e7\u00f5es geom\u00e9tricas atr\u00e1s indicadas,<br \/>a) um segmento de reta \u00e9 transformado noutro congruente; (<span style=\"color: #0000ff;\">V<\/span>)<br \/>b) um \u00e2ngulo \u00e9 transformado noutro de amplitude diferente; (<span style=\"color: #0000ff;\">F<\/span>)<br \/>c) uma semirreta \u00e9 transformada noutra semirreta com a mesma dire\u00e7\u00e3o e sentido; (<span style=\"color: #0000ff;\">F<\/span>)<br \/>d) cada figura \u00e9 transformada noutra congruente; (<span style=\"color: #0000ff;\">V<\/span>)<br \/>e) h\u00e1 pontos que se mant\u00eam fixos. (<span style=\"color: #0000ff;\">F<\/span>)<br \/>f) um segmento de reta \u00e9 transformado noutro que lhe \u00e9 paralelo. (<span style=\"color: #0000ff;\">F<\/span>)<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23954' onClick='GTTabs_show(0,23954)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa os mosaicos e os vetores \\({\\vec a}\\) e \\({\\vec b}\\). Relaciona com \\({\\vec a}\\) e \\({\\vec b}\\) o vetor que define a transla\u00e7\u00e3o que transforma:a) a figura A na F;b)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23958,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,685],"tags":[424,67,686,690,691,381,688],"series":[],"class_list":["post-23954","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-isometria","tag-reflexao-axial","tag-reflexao-deslizante","tag-translacao","tag-vetores"],"views":217,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag098-T10_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23954","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=23954"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23954\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23958"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23954"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23954"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23954"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23954"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}