document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124582>Question 1124582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Points A(-1,0),B(3,7),and C(5,-2) are the midpoints of the sides YZ, ZX AND XY of triangle XYZ. find the equation  of the line XY.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740927 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=740927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Assuming that the given points are midpoints of the RESPECTIVE sides of the triangle, A is the midpoint of YZ, B is the midpoint of XZ, and C is the midpoint of XY.<br><BR>\n" );
document.write( "Any line joining the midpoints of two sides of a triangle is parallel to the third side of the triangle and half the length of that third side.  That means<BR>\n" );
document.write( "(1) YZ is parallel to BC and twice the length of BC;<BR>\n" );
document.write( "(2) XZ is parallel to AC and twice the length of AC; and<BR>\n" );
document.write( "(3) XY is parallel to AB and twice the length of AB.<br><BR>\n" );
document.write( "From A to B is 4 units right and 7 units up; so point X is 4 units right and 7 units up from C, and point Y is 4 units left and 7 units down from C.<br><BR>\n" );
document.write( "From A to C is 6 units right and 2 units down; so point X is 6 units right and 2 units down from B, and point Z is 6 units left and 2 units up from B.<br><BR>\n" );
document.write( "From B to C is 2 units right and 9 units down; so point Y is 2 units right and 9 units down from A, and point Z is 2 units left and 9 units up from A.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C%0D%0Aline%28-1%2C0%2C5%2C-2%29%2Cline%285%2C-2%2C3%2C7%29%2Cline%283%2C7%2C-1%2C0%29%2C%0D%0Agreen%28line%28-3%2C9%2C9%2C5%29%29%2Cgreen%28line%289%2C5%2C1%2C-9%29%29%2Cgreen%28line%281%2C-9%2C-3%2C9%29%29%2C%0D%0Alocate%28-4%2C1%2C%22A%28-1%2C0%29%22%29%2Clocate%283%2C8%2C%22B%283%2C7%29%22%29%2Clocate%285%2C-2%2C%22C%285%2C-2%29%22%29%2C%0D%0Alocate%28-3%2C10%2CZ%29%2Clocate%289%2C5%2CX%29%2Clocate%281%2C-9%2CY%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ZA and AY are parallel to and the same length as BC<BR>\n" );
document.write( "ZB and BX are parallel to and the same length as AC<BR>\n" );
document.write( "YC and CX are parallel to and the same length as AB<br><BR>\n" );
document.write( "It should be easy to determine the coordinates of X, Y, and Z.<br><BR>\n" );
document.write( "Of course, the problem doesn't require us to do all that.  It only asks for the equation of line XY; and we can find that with far less work.<br><BR>\n" );
document.write( "I only demonstrated the process so you will be able to solve similar problems where you are asked to find the vertices of triangle XYZ.<br><BR>\n" );
document.write( "Using ideas discussed above, we know the line XY passes through C(5,-2) and has the same slope as AB.<br><BR>\n" );
document.write( "The slope of AB is 7/4 (\"right 4, up 7\" from above).  So one form of the equation of line XY is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2+=+%287%2F4%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y%2B2+=+%287%2F4%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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