document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=535938>Question 535938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Quadrilateral NORA has vertices N(3,2) O(7,0), R(11,2) an A(7,4). Use coordinate geometry to prove that quadrilateral NORA is a rhombus. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352037 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=352037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Quadrilateral NORA has vertices N(3,2) O(7,0), R(11,2) an A(7,4). Use coordinate geometry to prove that quadrilateral NORA is a rhombus.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C220%2C-5%2C15%2C-5%2C6%2C+graph%28400%2C220%2C-5%2C15%2C-5%2C6%29%2C%0D%0Acircle%283%2C2%2C.2%29%2C+circle%287%2C0%2C.2%29%2C+circle%2811%2C2%2C.2%29%2C+circle%287%2C4%2C.2%29%2C%0D%0Alocate%283.5%2C2.5%2C%22N%283%2C2%29%22%29%2C+locate%287.5%2C1%2C%22O%287%2C0%29%22%29%2C+locate%2811.2%2C2.5%2C%22R%2811%2C2%29%22%29%2C+locate%287.5%2C4.5%2C%22A%287%2C4%29%22%29%2C+%0D%0A%0D%0Agreen%28line%283%2C2%2C7%2C0%29%2C+line%287%2C0%2C11%2C2%29%2C+line%2811%2C2%2C7%2C4%29%2C+line%287%2C4%2C3%2C2%29%29%0D%0A%0D%0A%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "We prove that all 4 sides are the same length, using the distance formula:\r<BR>\n" );
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document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NO = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%287-3%29%5E2%2B%280-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%287-3%29%5E2%2B%280-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%5E2%2B%28-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%284%5E2%2B%28-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2B4%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2A5%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%285%29 ALIGN=MIDDLE  ALT=\"2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "OR = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%282-0%29%5E2%2B%2811-7%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%282-0%29%5E2%2B%2811-7%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%5E2%2B4%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%282%5E2%2B4%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2B16%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2A5%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%285%29 ALIGN=MIDDLE  ALT=\"2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "RA = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%287-11%29%5E2%2B%284-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%287-11%29%5E2%2B%284-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-4%29%5E2%2B2%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-4%29%5E2%2B2%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2B4%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2A5%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%285%29 ALIGN=MIDDLE  ALT=\"2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "AN = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%287-3%29%5E2%2B%284-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%287-3%29%5E2%2B%284-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%5E2%2B2%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%284%5E2%2B2%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2B4%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2A5%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%285%29 ALIGN=MIDDLE  ALT=\"2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "All four sides are of equal length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%285%29 ALIGN=MIDDLE  ALT=\"2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Edwin</pre>  </SPAN>\n" );
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