document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189504>Question 1189504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The vertices of a triangle are at A(-3, -2), B(2, 1) and C(6, 5). Find the length of the altitude <BR>\n" );
document.write( "from the vertex C and the length of side AB. Then compute for the area of the triangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820980 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The vertices of a triangle are at <BR>\n" );
document.write( "A(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "B(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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( "C(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
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document.write( "the length of side AB or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to the distance between A and B\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28%282-%28-3%29%29%5E2%2B%281-%28-2%29%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"c=sqrt%28%282-%28-3%29%29%5E2%2B%281-%28-2%29%29%5E2%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=c=sqrt%2834%29 ALIGN=MIDDLE  ALT=\"c=sqrt%2834%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5.831 ALIGN=MIDDLE  ALT=\"c=5.831\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "height to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > lie on a line perpendicular to AB and passes through C\r<BR>\n" );
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document.write( "use coordinates of A and B   first to find a slope of the line passing through A and B \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%281%2B2%29%2F%282%2B3%29=3%2F5 ALIGN=MIDDLE  ALT=\"m=%281%2B2%29%2F%282%2B3%29=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then line is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=%283%2F5%29%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=%283%2F5%29%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >........use slope and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1=%283%2F5%29%28x-2%29 ALIGN=MIDDLE  ALT=\"y-1=%283%2F5%29%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=%283%2F5%29x-2%283%2F5%29%2B1 ALIGN=MIDDLE  ALT=\"y=%283%2F5%29x-2%283%2F5%29%2B1\"   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+-+1%2F5 ALIGN=MIDDLE  ALT=\"y=%283%2F5%29x+-+1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then, a line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=perpendicular ALIGN=MIDDLE  ALT=\"perpendicular\"   DISABLED_style= \"max-width:90%; height:auto;\" > to AB will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=+-1%2F%283%2F5%29=-5%2F3 ALIGN=MIDDLE  ALT=\"m=+-1%2F%283%2F5%29=-5%2F3\"   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=y-y%5B1%5D=%28-5%2F3%29%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=%28-5%2F3%29%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......use slope and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=%28-5%2F3%29%28x-6%29 ALIGN=MIDDLE  ALT=\"y-5=%28-5%2F3%29%28x-6%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=%28-5%2F3%29%28x-6%29%2B5 ALIGN=MIDDLE  ALT=\"y=%28-5%2F3%29%28x-6%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-+%285+%2F3%29x%2B15 ALIGN=MIDDLE  ALT=\"y=+-+%285+%2F3%29x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find intersection point\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29x+-+1%2F5=-+%285+%2F3%29x%2B15 ALIGN=MIDDLE  ALT=\"%283%2F5%29x+-+1%2F5=-+%285+%2F3%29x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solving it, you get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+114%2F17 ALIGN=MIDDLE  ALT=\"x+=+114%2F17\"   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=y=+-+%285+%2F3%29%28114%2F17%29%2B15 ALIGN=MIDDLE  ALT=\"y=+-+%285+%2F3%29%28114%2F17%29%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+65%2F17 ALIGN=MIDDLE  ALT=\"y+=+65%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "convert to decimal:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6.706 ALIGN=MIDDLE  ALT=\"x+=+6.706\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3.824 ALIGN=MIDDLE  ALT=\"y+=+3.824\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "height is distance between C and intersection point\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=sqrt%28%286-6.706%29%5E2%2B%285-3.824%29%5E2%29 ALIGN=MIDDLE  ALT=\"h=sqrt%28%286-6.706%29%5E2%2B%285-3.824%29%5E2%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=h=+4sqrt%282%2F17%29=1.372 ALIGN=MIDDLE  ALT=\"h=+4sqrt%282%2F17%29=1.372\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Area:\r<BR>\n" );
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document.write( "if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+1.372 ALIGN=MIDDLE  ALT=\"h+=+1.372\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5.831 ALIGN=MIDDLE  ALT=\"c=5.831\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the area will be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+%281%2F2%29%2A5.831%2A1.372 ALIGN=MIDDLE  ALT=\"A=+%281%2F2%29%2A5.831%2A1.372\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4.000066 ALIGN=MIDDLE  ALT=\"A=4.000066\"   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 ALIGN=MIDDLE  ALT=\"A+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > square units\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%28-3%2C-2%2C.12%29%2Ccircle%282%2C1%2C.12%29%2Ccircle%286%2C5%2C.12%29%2C%0D%0Alocate%28-3%2C-2%2CA%29%2Clocate%282%2C1%2CB%29%2Clocate%286%2C5.5%2CC%29%2Clocate%286.5%2C5%2Ch%29%2C%0D%0Agreen%28line%28-3%2C-2%2C2%2C1%29%29%2Cgreen%28line%28-3%2C-2%2C6%2C5%29%29%2Cgreen%28line%286%2C5%2C2%2C1%29%29%2C%0D%0Acircle%286.706%2C3.824%2C.12%29%2C+blue%28line%286%2C5%2C6.706%2C3.824%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F5%29x+-+1%2F5%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );