document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122273>Question 122273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Points X (-1,1),Y (3,5), and Z (17,1), are the coordinates of three vertices of a parallelogram. What are the possible coordinates of W, the fourth vertex? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89775 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the coordinates of W be (h,k).<BR>\n" );
document.write( "The opposite sides of a parallelogram are parallel and hence their slopes must be equal.<BR>\n" );
document.write( "Slope of WX = Slope of YZ<BR>\n" );
document.write( "i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k-1%29%2F%28h-%28-1%29%29+=+%285+-+1%29%2F%283+-+17%29 ALIGN=MIDDLE  ALT=\"%28k-1%29%2F%28h-%28-1%29%29+=+%285+-+1%29%2F%283+-+17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k-1%29%2F%28h%2B1%29+=+-4%2F14+=+-2%2F7 ALIGN=MIDDLE  ALT=\"%28k-1%29%2F%28h%2B1%29+=+-4%2F14+=+-2%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28k-1%29+=+-2%28h%2B1%29 ALIGN=MIDDLE  ALT=\"7%28k-1%29+=+-2%28h%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h+%2B+7k+=+5%29 ALIGN=MIDDLE  ALT=\"2h+%2B+7k+=+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > __________ (1)\r<BR>\n" );
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document.write( "Slope of ZW = Slope of XY<BR>\n" );
document.write( "i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k-1%29%2F%28h-17%29+=+%285-1%29%2F%283-%28-1%29%29 ALIGN=MIDDLE  ALT=\"%28k-1%29%2F%28h-17%29+=+%285-1%29%2F%283-%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k-1%29%2F%28h-17%29+=+4%2F4+=+1 ALIGN=MIDDLE  ALT=\"%28k-1%29%2F%28h-17%29+=+4%2F4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k-1%29+=+%28h-17%29 ALIGN=MIDDLE  ALT=\"%28k-1%29+=+%28h-17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+-+k+=+16 ALIGN=MIDDLE  ALT=\"h+-+k+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > _________ (2)\r<BR>\n" );
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document.write( "Solving (1) and (2)<BR>\n" );
document.write( "h = 13<BR>\n" );
document.write( "k = -3\r<BR>\n" );
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document.write( "Hence, the coordinates of W are (13, -3). </SPAN>\n" );
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