{"id":7100,"date":"2011-10-23T18:35:26","date_gmt":"2011-10-23T17:35:26","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7100"},"modified":"2022-01-15T03:00:58","modified_gmt":"2022-01-15T03:00:58","slug":"tracar-duas-retas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7100","title":{"rendered":"Tra\u00e7ar duas retas"},"content":{"rendered":"<p><ul id='GTTabs_ul_7100' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7100' class='GTTabs_curr'><a  id=\"7100_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7100' ><a  id=\"7100_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_7100'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Constr\u00f3i num mesmo referencial as retas de equa\u00e7\u00f5es $3x+y=1$ e $-2x+y=6$.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7100' onClick='GTTabs_show(1,7100)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7100'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Comecemos por resolver as equa\u00e7\u00f5es em ordem a y:<\/p>\n<ul>\n<li>\u00a0$3x+y=1\\Leftrightarrow y=-3x+1$<\/li>\n<li>$-2x+y=6\\Leftrightarrow y=2x+6$<\/li>\n<\/ul>\n<p>Determinemos, seguidamente, as coordenadas de dois pontos de cada uma dessas retas:<\/p>\n<table class=\" aligncenter\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td>\n<table class=\"aligncenter\" style=\"width: 80%;\" border=\"1\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #516ceb;\">$x$<\/td>\n<td style=\"text-align: center; background-color: #516ceb;\">$y=-3x+1$<\/td>\n<td style=\"text-align: center; background-color: #516ceb;\">Ponto<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$0$<\/td>\n<td style=\"text-align: center;\">$1$<\/td>\n<td style=\"text-align: center;\">$A (0,1)$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$2$<\/td>\n<td style=\"text-align: center;\">$-5$<\/td>\n<td style=\"text-align: center;\">$B (2,-5)$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td><\/td>\n<td>\n<table class=\"aligncenter\" style=\"width: 80%;\" border=\"1\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #50d758;\">$x$<\/td>\n<td style=\"text-align: center; background-color: #50d758;\">$y=2x+6$<\/td>\n<td style=\"text-align: center; background-color: #50d758;\">Ponto<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$0$<\/td>\n<td style=\"text-align: center;\">$6$<\/td>\n<td style=\"text-align: center;\">$C (0,6)$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$-3$<\/td>\n<td style=\"text-align: center;\">$0$<\/td>\n<td style=\"text-align: center;\">$D (-3,0)$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\">\u00ad<br \/>\n<script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":474,\r\n\"height\":537,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 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