document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85404>Question 85404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really need help with this one, can someone please help me\r<BR>\n" );
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document.write( "Use coordinate geometry to prove that the quadrilateral OPQR with vertices O(0,0),P(9,3),Q(9,8), and R(-3,4) is an isosceles trapezoid. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61590 by </B><A HREF=/tutors/aboutme.mpl?userid=scianci><B>scianci(186)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scianci><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=61590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the lengths of the 4 sides:\r<BR>\n" );
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document.write( "OP = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%280+-+9%29%5E2+%2B+%280+-+3%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%280+-+9%29%5E2+%2B+%280+-+3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-9%29%5E2+%2B+%28-3%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-9%29%5E2+%2B+%28-3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881+%2B+9%29 ALIGN=MIDDLE  ALT=\"sqrt%2881+%2B+9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2890%29 ALIGN=MIDDLE  ALT=\"sqrt%2890%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "PQ = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%289+-+9%29%5E2+%2B+%283+-+8%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%289+-+9%29%5E2+%2B+%283+-+8%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%280%29%5E2+%2B+%28-5%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%280%29%5E2+%2B+%28-5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%280+%2B+25%29 ALIGN=MIDDLE  ALT=\"sqrt%280+%2B+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = 5\r<BR>\n" );
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document.write( "QR = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%289+-+%28-3%29%29%5E2+%2B+%288+-+4%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%289+-+%28-3%29%29%5E2+%2B+%288+-+4%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%5E2+%2B+4%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2812%5E2+%2B+4%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144+%2B+16%29 ALIGN=MIDDLE  ALT=\"sqrt%28144+%2B+16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28160%29 ALIGN=MIDDLE  ALT=\"sqrt%28160%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "RO = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28-3%29+-+0%29%5E2+%2B+%284+-+0%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28-3%29+-+0%29%5E2+%2B+%284+-+0%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-3%29%5E2+%2B+4%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-3%29%5E2+%2B+4%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289+%2B+16%29 ALIGN=MIDDLE  ALT=\"sqrt%289+%2B+16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   = 5\r<BR>\n" );
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document.write( "Since PQ = RO, this proves that it's isosceles. To prove that it's a trapezoid, consider the slope of each side:\r<BR>\n" );
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document.write( "slope OP = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280+-+9%29%2F%280+-+3%29 ALIGN=MIDDLE  ALT=\"%280+-+9%29%2F%280+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "         = -9/-3 = 3\r<BR>\n" );
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document.write( "slope PQ = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289+-+9%29%2F%283+-+8%29 ALIGN=MIDDLE  ALT=\"%289+-+9%29%2F%283+-+8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "         = 0/-5 = 0\r<BR>\n" );
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document.write( "slope QR = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289+-+%28-3%29%29%2F%288+-+4%29 ALIGN=MIDDLE  ALT=\"%289+-+%28-3%29%29%2F%288+-+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "         = 12/4 = 3\r<BR>\n" );
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document.write( "slope RO = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280+-+%28-3%29%29%2F%280+-+4%29 ALIGN=MIDDLE  ALT=\"%280+-+%28-3%29%29%2F%280+-+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "         = 3/-4 = -3/4\r<BR>\n" );
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document.write( "Since OP and QR have equal slopes, they are parallel. Furthermore, since they are the only sides that are parallel, by definition that makes the quadrilateral a trapezoid. </SPAN>\n" );
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