document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1079613>Question 1079613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graph a quadrilateral with points of A(6,5), B(-3,-1), C(-1,-4), D(8,2)<BR>\n" );
document.write( "what type of quadrilateral is ABCD? Use slope to justify my answer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693843 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=693843\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graph:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/F9Q4oSf.png\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's find the slopes of the four sides (AB, BC, CD, DA)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Slope of AB\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-1+-+5%29%2F%28-3+-+6%29 ALIGN=MIDDLE  ALT=\"m+=+%28-1+-+5%29%2F%28-3+-+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-6%29%2F%28-9%29 ALIGN=MIDDLE  ALT=\"m+=+%28-6%29%2F%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+2%2F3 ALIGN=MIDDLE  ALT=\"m+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Slope of BC\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-4+-+%28-1%29%29%2F%28-1+-+%28-3%29%29 ALIGN=MIDDLE  ALT=\"m+=+%28-4+-+%28-1%29%29%2F%28-1+-+%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-3%2F2 ALIGN=MIDDLE  ALT=\"m+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Slope of CD\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%282+-+%28-4%29%29%2F%288+-+%28-1%29%29 ALIGN=MIDDLE  ALT=\"m+=+%282+-+%28-4%29%29%2F%288+-+%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%286%29%2F%289%29 ALIGN=MIDDLE  ALT=\"m+=+%286%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+2%2F3 ALIGN=MIDDLE  ALT=\"m+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Slope of DA\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%285+-+2%29%2F%286+-+8%29 ALIGN=MIDDLE  ALT=\"m+=+%285+-+2%29%2F%286+-+8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%283%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"m+=+%283%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-3%2F2 ALIGN=MIDDLE  ALT=\"m+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In summary so far, we have\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Slope of AB = 2/3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Slope of BC = -3/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Slope of CD = 2/3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Slope of DA = -3/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice how the opposite sides have equal slopes (AB and CD have same slope; BC and DA have same slope). This means we have parallel opposite sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Parallel lines have equal slopes.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So this figure is a parallelogram. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "More specifically this figure is a rectangle because the sides are perpendicular. How do we know this? Because the product of the non-equal adjacent slopes is -1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For instance, (slope of AB)*(slope of BC) = (2/3)*(-3/2) = -1. This particular example shows how AB is perpendicular to BC. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the adjacent sides are perpendicular, four right angles form to have this figure be a rectangle.\r<BR>\n" );
document.write( "\n" );
document.write( "-----------------------------------------------------------------------<BR>\n" );
document.write( "-----------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Final Answer: <font size=4 color=red>The figure is a rectangle</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );