document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=805403>Question 805403</A>: <I><SPAN STYLE=\"word-break: break-all;\"> are the lines parallel, perpendicular, or neither? AB: A(0,2) B(3,4) C(2,7) D(-1,5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #485223 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=485223\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> AB is parallel to CD and BC is parallel to AD.<BR>\n" );
document.write( "There are no perpendicular lines.<BR>\n" );
document.write( "ABCD is a parallelogram, but not a rectangle.<BR>\n" );
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document.write( "Parallel lines have the same slope. Perpendicular lines have slopes whose product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   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=%284-2%29%2F%283-0%29=2%2F3 ALIGN=MIDDLE  ALT=\"%284-2%29%2F%283-0%29=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and slope of DC = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287-5%29%2F%283-0%29=2%2F%282%2B1%29=2%2F3 ALIGN=MIDDLE  ALT=\"%287-5%29%2F%283-0%29=2%2F%282%2B1%29=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both slopes are the same, so AB is parallel to DC <BR>\n" );
document.write( "slope of BC = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287-4%29%2F%282-3%29=3%2F%28-1%29=-3 ALIGN=MIDDLE  ALT=\"%287-4%29%2F%282-3%29=3%2F%28-1%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and slope of DA = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-2%29%2F%28-1-0%29=3%2F%28-1%29=-3 ALIGN=MIDDLE  ALT=\"%285-2%29%2F%28-1-0%29=3%2F%28-1%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both slopes are the same, so BC is parallel to DA.<BR>\n" );
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document.write( "The product of the slopes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%28-3%29=-2%3C%3E-1 ALIGN=MIDDLE  ALT=\"%282%2F3%29%28-3%29=-2%3C%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > so there are no perpendicular lines in ABCD.<BR>\n" );
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document.write( "From the drawing (see below) I can tell that it is not a rhombus, because the sides have different length, so diagonals AC and BD are not perpendicular.<BR>\n" );
document.write( "AB and CD are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2813%29 ALIGN=MIDDLE  ALT=\"sqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long.<BR>\n" );
document.write( "BC and DA are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C6%2C-1%2C9%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28line%280%2C2%2C3%2C4%29%29%2Cblue%28line%282%2C7%2C3%2C4%29%29%2C%0D%0Ablue%28line%282%2C7%2C-1%2C5%29%29%2Cblue%28line%280%2C2%2C-1%2C5%29%29%2C%0D%0Agreen%28line%280%2C2%2C2%2C7%29%29%2Cgreen%28line%283%2C4%2C-1%2C5%29%29%2C%0D%0Alocate%280.1%2C2%2CA%29%2Clocate%283.1%2C4%2CB%29%2C%0D%0Alocate%282.1%2C7.5%2CC%29%2Clocate%28-1.3%2C5.5%2CD%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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