document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=835146>Question 835146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagonals of quadrilateral EFGH intersect at D(-1,4). Two vertices of EFGH are E(2,7) and F(-3,5). What must be the coordinates of G and H to ensure that EFGH is a parallelogram? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503391 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=503391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28750%2F3%2C300%2C-6%2C4%2C-2%2C10%2C%0D%0A%0D%0Agrid%281%29%2C%0D%0A%0D%0Acircle%28-1%2C4%2C0.15%29%2Ccircle%28-1%2C4%2C0.13%29%2Ccircle%28-1%2C4%2C0.11%29%2Ccircle%28-1%2C4%2C0.09%29%2Ccircle%28-1%2C4%2C0.07%29%2Ccircle%28-1%2C4%2C0.05%29%2Ccircle%28-1%2C4%2C0.03%29%2Ccircle%28-1%2C4%2C0.01%29%2C%0D%0Aline%282%2C7%2C-3%2C5%29%2C%0D%0Acircle%28-3%2C5%2C0.15%29%2Ccircle%28-3%2C5%2C0.13%29%2Ccircle%28-3%2C5%2C0.11%29%2Ccircle%28-3%2C5%2C0.09%29%2Ccircle%28-3%2C5%2C0.07%29%2Ccircle%28-3%2C5%2C0.05%29%2Ccircle%28-3%2C5%2C0.03%29%2Ccircle%28-3%2C5%2C0.01%29%2C%0D%0Alocate%28-3.1%2C5%2CF%29%2C%0D%0A%0D%0Acircle%282%2C7%2C0.15%29%2Ccircle%282%2C7%2C0.13%29%2Ccircle%282%2C7%2C0.11%29%2Ccircle%282%2C7%2C0.09%29%2Ccircle%282%2C7%2C0.07%29%2Ccircle%282%2C7%2C0.05%29%2Ccircle%282%2C7%2C0.03%29%2Ccircle%282%2C7%2C0.01%29%2C%0D%0A%0D%0A%0D%0Alocate%28-1.4%2C4%2CD%29%2Clocate%281.6%2C7%2CE%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Since the diagonals of a parallelogram bisect each other we know <BR>\n" );
document.write( "that ED is half a diagonal.  So we draw in half-diagonal ED.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28750%2F3%2C300%2C-6%2C4%2C-2%2C10%2C%0D%0Agreen%28line%282%2C7%2C-1%2C4%29%29%2C%0D%0Agrid%281%29%2C%0D%0A%0D%0Acircle%28-1%2C4%2C0.15%29%2Ccircle%28-1%2C4%2C0.13%29%2Ccircle%28-1%2C4%2C0.11%29%2Ccircle%28-1%2C4%2C0.09%29%2Ccircle%28-1%2C4%2C0.07%29%2Ccircle%28-1%2C4%2C0.05%29%2Ccircle%28-1%2C4%2C0.03%29%2Ccircle%28-1%2C4%2C0.01%29%2C%0D%0Aline%282%2C7%2C-3%2C5%29%2C%0D%0Acircle%28-3%2C5%2C0.15%29%2Ccircle%28-3%2C5%2C0.13%29%2Ccircle%28-3%2C5%2C0.11%29%2Ccircle%28-3%2C5%2C0.09%29%2Ccircle%28-3%2C5%2C0.07%29%2Ccircle%28-3%2C5%2C0.05%29%2Ccircle%28-3%2C5%2C0.03%29%2Ccircle%28-3%2C5%2C0.01%29%2C%0D%0Alocate%28-3.4%2C5%2CF%29%2C%0D%0A%0D%0Acircle%282%2C7%2C0.15%29%2Ccircle%282%2C7%2C0.13%29%2Ccircle%282%2C7%2C0.11%29%2Ccircle%282%2C7%2C0.09%29%2Ccircle%282%2C7%2C0.07%29%2Ccircle%282%2C7%2C0.05%29%2Ccircle%282%2C7%2C0.03%29%2Ccircle%282%2C7%2C0.01%29%2C%0D%0A%0D%0A%0D%0Alocate%28-1.4%2C4%2CD%29%2Clocate%281.6%2C7%2CE%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Going from E to D is going left 3 units and down 3 units, so to<BR>\n" );
document.write( "extend the half diagonal to finish the full diagonal EG, from D we go <BR>\n" );
document.write( "left 3 units and down 3 units, and arrive at (-4,1), and label it G.<BR>\n" );
document.write( "Then we draw side FG \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28750%2F3%2C300%2C-6%2C4%2C-2%2C10%2C%0D%0Agreen%28line%282%2C7%2C-4%2C1%29%29%2Clocate%28-3.8%2C1%2CG%29%2C%0D%0Agrid%281%29%2C%0D%0A%0D%0Acircle%28-1%2C4%2C0.15%29%2Ccircle%28-1%2C4%2C0.13%29%2Ccircle%28-1%2C4%2C0.11%29%2Ccircle%28-1%2C4%2C0.09%29%2Ccircle%28-1%2C4%2C0.07%29%2Ccircle%28-1%2C4%2C0.05%29%2Ccircle%28-1%2C4%2C0.03%29%2Ccircle%28-1%2C4%2C0.01%29%2C%0D%0Aline%282%2C7%2C-3%2C5%29%2C%0D%0Acircle%28-3%2C5%2C0.15%29%2Ccircle%28-3%2C5%2C0.13%29%2Ccircle%28-3%2C5%2C0.11%29%2Ccircle%28-3%2C5%2C0.09%29%2Ccircle%28-3%2C5%2C0.07%29%2Ccircle%28-3%2C5%2C0.05%29%2Ccircle%28-3%2C5%2C0.03%29%2Ccircle%28-3%2C5%2C0.01%29%2C%0D%0Alocate%28-3.3%2C5%2CF%29%2C%0D%0A%0D%0Acircle%282%2C7%2C0.15%29%2Ccircle%282%2C7%2C0.13%29%2Ccircle%282%2C7%2C0.11%29%2Ccircle%282%2C7%2C0.09%29%2Ccircle%282%2C7%2C0.07%29%2Ccircle%282%2C7%2C0.05%29%2Ccircle%282%2C7%2C0.03%29%2Ccircle%282%2C7%2C0.01%29%2C%0D%0A%0D%0Aline%28-4%2C1%2C-3%2C5%29%2C%0D%0Acircle%28-4%2C1%2C0.15%29%2Ccircle%28-4%2C1%2C0.13%29%2Ccircle%28-4%2C1%2C0.11%29%2Ccircle%28-4%2C1%2C0.09%29%2Ccircle%28-4%2C1%2C0.07%29%2Ccircle%28-4%2C1%2C0.05%29%2Ccircle%28-4%2C1%2C0.03%29%2Ccircle%28-4%2C1%2C0.01%29%2C%0D%0A%0D%0Alocate%28-1.4%2C4%2CD%29%2Clocate%281.6%2C7.7%2CE%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We could finish by doing the same with the other diagonal. <BR>\n" );
document.write( "But we can also just realize that going from F to E is <BR>\n" );
document.write( "going right 5 units and up 2 units. So to find the point H,<BR>\n" );
document.write( "from G we go right 5 units and up 2 units, and arrive at <BR>\n" );
document.write( "(1,3), and label it H. Then we draw sides GH and HE.\r<BR>\n" );
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document.write( "So G is (-4,1) and H is (1,3)\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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