document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031169>Question 1031169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two vertices of a triangle are (2,4) and (-2,3) and the area is 2 square units, the locus of the third vertex is?\r<BR>\n" );
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document.write( "What should be the answer here? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645903 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=645903\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let distance between those two points be the base for the triangle.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%282-%28-2%29%29%5E2%2B%284-3%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%282-%28-2%29%29%5E2%2B%284-3%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%2816%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2B1%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%2817%29 ALIGN=MIDDLE  ALT=\"sqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "An altitude could intersect the base ANYWHERE and you want to be sure that the altitude length will give area of 2 square units.  Let a be the altitude length.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29sqrt%2817%29%2Aa=2 ALIGN=MIDDLE  ALT=\"%281%2F2%29sqrt%2817%29%2Aa=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Asqrt%2817%29=4 ALIGN=MIDDLE  ALT=\"a%2Asqrt%2817%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4%2Fsqrt%2817%29 ALIGN=MIDDLE  ALT=\"a=4%2Fsqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "THE PROBLEM HAS INFINITELY MANY SOLUTIONS.  The altitude must be perpendicular to the base and be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fsqrt%2817%29 ALIGN=MIDDLE  ALT=\"4%2Fsqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "BASE<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=%28%284-3%29%2F%282-%28-2%29%29%29%28x-%28-2%29%29 ALIGN=MIDDLE  ALT=\"y-3=%28%284-3%29%2F%282-%28-2%29%29%29%28x-%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=%281%2F4%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"y-3=%281%2F4%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and perpendicular line containing the altitude is ,  if you choose one endpoint on the altitude to be  (2,4),  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=-4%28x-2%29 ALIGN=MIDDLE  ALT=\"y-4=-4%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4x%2B8%2B4 ALIGN=MIDDLE  ALT=\"y=-4x%2B8%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4x%2B12 ALIGN=MIDDLE  ALT=\"y=-4x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >------line containing the altitude at base endpoint (2,4).\r<BR>\n" );
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document.write( "An unknown point  (x,-4x+12) must be distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2817%29 ALIGN=MIDDLE  ALT=\"sqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from point (2,4).<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-2%29%5E2%2B%28-4x%2B12-4%29%5E2%29=sqrt%2817%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-2%29%5E2%2B%28-4x%2B12-4%29%5E2%29=sqrt%2817%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%28x-2%29%5E2%2B%28-4%2B8%29%5E2%29=sqrt%2817%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-2%29%5E2%2B%28-4%2B8%29%5E2%29=sqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B%288-4x%29%5E2=17 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B%288-4x%29%5E2=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B4%2B64-64x%2B16x%5E2=17 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B4%2B64-64x%2B16x%5E2=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17x%5E2-68x%2B68=17 ALIGN=MIDDLE  ALT=\"17x%5E2-68x%2B68=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17x%5E2-68x%2B57=0 ALIGN=MIDDLE  ALT=\"17x%5E2-68x%2B57=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2868%2B-+sqrt%2868%5E2-4%2A17%2A57%29%29%2F%282%2A17%29 ALIGN=MIDDLE  ALT=\"x=%2868%2B-+sqrt%2868%5E2-4%2A17%2A57%29%29%2F%282%2A17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2868%2B-+sqrt%28748%29%29%2F%282%2A17%29 ALIGN=MIDDLE  ALT=\"x=%2868%2B-+sqrt%28748%29%29%2F%282%2A17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2868%2B-+2sqrt%28187%29%29%2F%282%2A17%29 ALIGN=MIDDLE  ALT=\"x=%2868%2B-+2sqrt%28187%29%29%2F%282%2A17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=34%2B-+sqrt%28187%29%29%2F17%29 ALIGN=MIDDLE  ALT=\"highlight%28x=34%2B-+sqrt%28187%29%29%2F17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----Use this the find the corresponding y coordinate values.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=34%2B-+sqrt%2811%2A17%29%29%2F17 ALIGN=MIDDLE  ALT=\"x=34%2B-+sqrt%2811%2A17%29%29%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" >------not simplifiable further </SPAN>\n" );
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