document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40985>Question 40985</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534494498/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Determine the point A(x,y) so that the points A(x,y), B(0,3) C(1,0), D(7,2) will be the vertices of a parallelogram.\r<BR>\n" );
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document.write( "I think it is A(5,6), but I am not sure.  Thank you for your help.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26424 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=26424\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Slope of CD = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-0%29%2F%287-1%29+=+1%2F3 ALIGN=MIDDLE  ALT=\"%282-0%29%2F%287-1%29+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Slope of BC = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-0%29%2F%280-1%29+=+-3 ALIGN=MIDDLE  ALT=\"%283-0%29%2F%280-1%29+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Slope of AB = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-3%29%2F%28x-0%29+=+%28y-3%29%2Fx ALIGN=MIDDLE  ALT=\"%28y-3%29%2F%28x-0%29+=+%28y-3%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Slope of AD = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-2%29%2F%28x-7%29 ALIGN=MIDDLE  ALT=\"%28y-2%29%2F%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As ABCD is a parallelogram so AB and CD are parallel and hence their slopes equal.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-3%29%2Fx+=+1%2F3 ALIGN=MIDDLE  ALT=\"%28y-3%29%2Fx+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "or 3(y-3) = x <BR>\n" );
document.write( "or x - 3y = -9 __________(1)\r<BR>\n" );
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document.write( "Also AD and BC are parallel and hence their slopes equal.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-2%29%2F%28x-7%29+=+-3 ALIGN=MIDDLE  ALT=\"%28y-2%29%2F%28x-7%29+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "or (y-2) = -3(x-7)  <BR>\n" );
document.write( "or y + 3x = 23 ____________(2)\r<BR>\n" );
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document.write( "Multiplying (2) by 3 and adding with (1) we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A3x+%2B+x+=+23%2A3+-+9+=+69+-+9+=+60 ALIGN=MIDDLE  ALT=\"3%2A3x+%2B+x+=+23%2A3+-+9+=+69+-+9+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or 10x = 60<BR>\n" );
document.write( "or x = 6 <BR>\n" );
document.write( "Then from (2) we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+23+-+3%2A6+=+5 ALIGN=MIDDLE  ALT=\"y+=+23+-+3%2A6+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence the coordinates of A are (6,5). </SPAN>\n" );
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