document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094532>Question 1094532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three points D(-5,6), E(2,-1), and F(x,0) are given. Find the value of X if DF=EF. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837934 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here is an alternative solution method, using a bit of geometry along with the algebra.<br><BR>\n" );
document.write( "If DF=EF, then F is on the perpendicular bisector of DE.<br><BR>\n" );
document.write( "The midpoint of DE is (-1.5,2.5), and its slope is -1.<br><BR>\n" );
document.write( "So F is on the line with slope 1 passing through (-1.5,2.5).  The point-slope form of the equation of that line is<br><BR>\n" );
document.write( "y-2.5 = 1(x+1.5)<br><BR>\n" );
document.write( "We know F is (x,0), so y is 0.  Substitute y=0 and solve to find x.<br><BR>\n" );
document.write( "0-2.5 = x+1.5<BR>\n" );
document.write( "-2.5-1.5 = x<BR>\n" );
document.write( "x = -4<br><BR>\n" );
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