document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016826>Question 1016826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> show that the points(1,-3),(3,2),(-2,4) are the vertices of an isosceles triangle and find its area. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #633205 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</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=633205\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Pick any two points to serve as a base for finding the area.\r<BR>\n" );
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document.write( "Points  (1,-3) and (3,2):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281-3%29%5E2%2B%28-3-2%29%5E2%29=sqrt%284%2B36%29=sqrt%2840%29=sqrt%284%2A10%29=highlight_green%282sqrt%2810%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The line containing those points is...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%282-%28-3%29%29%2F%283-1%29=5%2F3 ALIGN=MIDDLE  ALT=\"m=%282-%28-3%29%29%2F%283-1%29=5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2=%285%2F3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y-2=%285%2F3%29%28x-3%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-2=%285%2F3%29x-5 ALIGN=MIDDLE  ALT=\"y-2=%285%2F3%29x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=%285%2F3%29x-3%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=%285%2F3%29x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use that line, and the not-yet-used vertex point of  (-2,4).<BR>\n" );
document.write( "What is equation of the line perpendicular to the chosen base and containing point (-2,4)?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=-%283%2F5%29%28x-%28-2%29%29 ALIGN=MIDDLE  ALT=\"y-4=-%283%2F5%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-4=-%283%2F5%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"y-4=-%283%2F5%29%28x%2B2%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-4=-%283%2F5%29x-6%2F5 ALIGN=MIDDLE  ALT=\"y-4=-%283%2F5%29x-6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F5%29x-6%2F5%2B4 ALIGN=MIDDLE  ALT=\"y=-%283%2F5%29x-6%2F5%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=-%283%2F5%29x-6%2F5%2B20%2F5 ALIGN=MIDDLE  ALT=\"y=-%283%2F5%29x-6%2F5%2B20%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=-%283%2F5%29x%2B14%2F5%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=-%283%2F5%29x%2B14%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What is the \"height\" of the triangle, using this point (-2,4) as one endpoint?<BR>\n" );
document.write( "Find the intersection point of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F5%29x%2B14%2F5 ALIGN=MIDDLE  ALT=\"y=-%283%2F5%29x%2B14%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F3%29x-3 ALIGN=MIDDLE  ALT=\"y=%285%2F3%29x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Skipping the steps here, that intersection point is  ( 87/34, 43/34 ).<BR>\n" );
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document.write( "The height you want is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=sqrt%28%2887%2F34-%28-2%29%29%5E2%2B%2843%2F34-4%29%5E2%29 ALIGN=MIDDLE  ALT=\"h=sqrt%28%2887%2F34-%28-2%29%29%5E2%2B%2843%2F34-4%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Simplify this as much as possible.\r<BR>\n" );
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document.write( "Your goal is to use area formula  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%282%2Asqrt%2810%29%29%2Ah ALIGN=MIDDLE  ALT=\"%281%2F2%29%282%2Asqrt%2810%29%29%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "To show that the triangle is isosceles, just use Distance Formula between the three segments. </SPAN>\n" );
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