document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253208>Question 253208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you find the coordinates of a triangle's vertices by just having the coordinates of its midpoints? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185440 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A, B, and C be the verticies of the triangle.<BR>\n" );
document.write( "By definition of midpoint, let <BR>\n" );
document.write( "(A+B)/2 = m1<BR>\n" );
document.write( "(A+C)/2 = m2<BR>\n" );
document.write( "(B+C)/2 = m3,<BR>\n" );
document.write( "where m1, m1, m3 are midpoints that I assume are given.<BR>\n" );
document.write( "Solving using a process called Gauss-Jordan Elimination, we get<BR>\n" );
document.write( "Coordinate A = m1 + m2 - m3<BR>\n" );
document.write( "Coordinate B = m1 - m2 + m3<BR>\n" );
document.write( "Coordinate C = -m1 + m2 + m3.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "EX: m1 =  (0,2), m2 = (3,0), m3 = (3,2)<BR>\n" );
document.write( "A = (0,2) + (3,0) - (3,2) = (0,0)<BR>\n" );
document.write( "B = (0,2) - (3,0) + (3,2) = (0,4)<BR>\n" );
document.write( "C = -(0,2) + (3,0) + (3,2) = (6,0)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "The three verticies are: (0,0) (6,0) (0,4). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );