{"id":41672,"date":"2017-11-04T11:23:43","date_gmt":"2017-11-04T10:23:43","guid":{"rendered":"http:\/\/www.valcon.it\/math\/?p=14470"},"modified":"2017-11-04T11:23:43","modified_gmt":"2017-11-04T10:23:43","slug":"esercizio-59","status":"publish","type":"post","link":"https:\/\/www.valcon.it\/pp\/esercizio-59\/","title":{"rendered":"Esercizio 59"},"content":{"rendered":"<blockquote><p>Scrivi l&#8217;equazione della retta r della figura e considera su r un punto C variabile.<\/p>\n<ol>\n<li>Determina il baricentro G del triangolo ABC e scrivi l&#8217;equazione del luogo descritto a G.<br \/>\nCalcola le coordinate di C quando G ha ascissa 3.<\/li>\n<li>Determina C nel primo quadrante in modo che <img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%5Coverline%7BAC%7D%3D%5Csqrt%7B17%7D\" alt=\"\\overline{AC}=\\sqrt{17}\" align=\"absmiddle\" \/> e trova l&#8217;ortocentro H di ABC.<\/li>\n<li>Trova C in modo il triangolo ABC sia isoscele, con base AB, e determina l&#8217;incentro di ABC.<\/li>\n<\/ol>\n<\/blockquote>\n<p><a href=\"http:\/\/www.valcon.it\/math\/wp-content\/uploads\/Esercizio-59_0.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-medium wp-image-14478\" src=\"http:\/\/www.valcon.it\/math\/wp-content\/uploads\/Esercizio-59_0-228x300.png\" alt=\"\" width=\"228\" height=\"300\" \/><\/a>Dati del problema<\/p>\n<ul>\n<li><img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=A%3D(1%2C0)\" alt=\"A=(1,0)\" align=\"absmiddle\" \/><\/li>\n<li><img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=B%3D(5%2C0)\" alt=\"B=(5,0)\" align=\"absmiddle\" \/><\/li>\n<li><img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=Q%3D(1%2C2)\" alt=\"Q=(1,2)\" align=\"absmiddle\" \/><\/li>\n<\/ul>\n<p>Costruzione<\/p>\n<ul>\n<li>r: <img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%5Cfrac%7By-y_0%7D%7By_Q-y_0%7D%3D%5Cfrac%7Bx-x_0%7D%7Bx_Q-x_0%7D\" alt=\"\\frac{y-y_0}{y_Q-y_0}=\\frac{x-x_0}{x_Q-x_0}\" align=\"absmiddle\" \/>, &#8230; r: <img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=y%3D2x\" alt=\"y=2x\" align=\"absmiddle\" \/><\/li>\n<li><img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=C%3D(x%2C2x)\" alt=\"C=(x,2x)\" align=\"absmiddle\" \/><\/li>\n<\/ul>\n<p>Quesiti<\/p>\n<ol>\n<li><img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=G%3D%5Cleft(%5Cfrac%7Bx_A%2Bx_B%2Bx_C%7D%7B3%7D%2C%5Cfrac%7By_A%2By_B%2By_C%7D%7B3%7D%5Cright)\" alt=\"G=\\left(\\frac{x_A+x_B+x_C}{3},\\frac{y_A+y_B+y_C}{3}\\right)\" align=\"absmiddle\" \/>, &#8230;, <img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=G%3D%5Cleft(%5Cfrac%7B1%7D%7B3%7Dx%2B2%2C%5Cfrac%7B2%7D%7B3%7Dx%5Cright)\" alt=\"G=\\left(\\frac{1}{3}x+2,\\frac{2}{3}x\\right)\" align=\"absmiddle\" \/><br \/>\nluogo(G,C): &#8230;, <img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=y%3D2x-4\" alt=\"y=2x-4\" align=\"absmiddle\" \/><br \/>\n<img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=x_G%3D3\" alt=\"x_G=3\" align=\"absmiddle\" \/>, &#8230;, <img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=C%3D(3%2C6)\" alt=\"C=(3,6)\" align=\"absmiddle\" \/><\/li>\n<li><img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%5Coverline%7BAC%7D%3D%5Csqrt%7B17%7D\" alt=\"\\overline{AC}=\\sqrt{17}\" align=\"absmiddle\" \/>, &#8230;, <img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=C%3D(2%2C4)\" alt=\"C=(2,4)\" align=\"absmiddle\" \/>, &#8230;, <img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=H%3D%5Cleft(2%20%2C%20%20%5Cfrac%7B3%7D%7B4%7D%5Cright)\" alt=\"H=\\left(2 , \\frac{3}{4}\\right)\" align=\"absmiddle\" \/><\/li>\n<li><img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%5Coverline%7BAC%7D%3D%5Coverline%7BBC%7D\" alt=\"\\overline{AC}=\\overline{BC}\" align=\"absmiddle\" \/>, &#8230;, <img decoding=\"async\" class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=C%3D(3%2C6)\" alt=\"C=(3,6)\" align=\"absmiddle\" \/><\/li>\n<\/ol>\n<hr \/>\n<hr \/>\n<p>Codifica: <a href=\"http:\/\/www.valcon.it\/math\/wp-content\/uploads\/es-59.zip\">Geogebra<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Scrivi l&#8217;equazione della retta r della figura e considera su r un punto C variabile. Determina il baricentro G del triangolo ABC e scrivi l&#8217;equazione del luogo descritto a G. Calcola le coordinate di C quando G ha ascissa 3. Determina C nel primo quadrante in modo che e trova l&#8217;ortocentro H di ABC. Trova &#8230; <a title=\"Esercizio 59\" class=\"read-more\" href=\"https:\/\/www.valcon.it\/pp\/esercizio-59\/\" aria-label=\"Per saperne di pi\u00f9 su Esercizio 59\">Leggi tutto<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[114,126],"tags":[],"class_list":["post-41672","post","type-post","status-publish","format-standard","hentry","category-calcolo","category-geogebra"],"_links":{"self":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts\/41672","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/comments?post=41672"}],"version-history":[{"count":0,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts\/41672\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/media?parent=41672"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/categories?post=41672"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/tags?post=41672"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}