document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374261>Question 374261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Triangle pqr has the given vertice classify the triangle  by its sides. then determine if it is a right triangle \r<BR>\n" );
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document.write( "p(2,0) q (6,6) and  r (12,2)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266362 by </B><A HREF=/tutors/aboutme.mpl?userid=Jk22><B>Jk22(389)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Jk22><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Jk22><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p(2,0) q (6,6) and  r (12,2)<BR>\n" );
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document.write( "side length : |pq|=|(6-2,6-0)|=|(4,6)|=sqrt(16+36)=sqrt(52)<BR>\n" );
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document.write( "|pr|=|(12-2,2-0)|=|(10,2)|=sqrt(104)\r<BR>\n" );
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document.write( "|qr|=|(12-6,2-6)|=|(6,-4)|=sqrt(36+16)|=sqrt(52)<BR>\n" );
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document.write( "two sides are equal, it's an isoceles triangle.<BR>\n" );
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document.write( "angles : (dot product, if a.b=0 the 2 vectors are orthogonal) <BR>\n" );
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document.write( "pq.pr=40+12<>0<BR>\n" );
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document.write( "pq.qr=4*6-6*4=0 (for verif : pr*qr=60-8<>0)<BR>\n" );
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document.write( "hence the triangle is rectangle and has a right angle in q.\r<BR>\n" );
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