document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110443>Question 1110443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can I find the orthocenter? I keep getting really big numbers like (30,15), but then the points would be far away from the triangle because the ordered pairs are (-6,3),(4,13) and (10,-5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725449 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=725449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I labeled the vertices A(-6,3), B(4,13), C(10,-5)\r<BR>\n" );
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document.write( "Side a connects B with C<BR>\n" );
document.write( "Side b connects A with C<BR>\n" );
document.write( "Side c connects A with B \r<BR>\n" );
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document.write( "Eqn for line coincident with side a:  y=-3x+25    (1)<BR>\n" );
document.write( "Eqn for line  coincident with side b:   y=(-1/2)x    (2)<BR>\n" );
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document.write( "Slope of perpendicular to (1):   1/3<BR>\n" );
document.write( "  y=(1/3)x+b    (b here is y-intercept) <BR>\n" );
document.write( "line passes through A(-6,3)<BR>\n" );
document.write( "  3 = (1/3)(-6) + b   —>  b = 5  —>   y=(1/3)x + 5   (1')\r<BR>\n" );
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document.write( " Slope of perpendicular  to (2):  2<BR>\n" );
document.write( "   y=2x + b  <BR>\n" );
document.write( "line passes through B(4,13)<BR>\n" );
document.write( "   13=2(4)+b  —>  b = 5 —>   y=2x+5   (2')\r<BR>\n" );
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document.write( "—\r<BR>\n" );
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document.write( "Lines (1') and (2') meet at the orthocenter.\r<BR>\n" );
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document.write( "         Where they meet, their x values AND y values must match:\r<BR>\n" );
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document.write( "               2x+5 = (1/3)x+5<BR>\n" );
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document.write( "    This only holds at x=0,  and there y=5    \r<BR>\n" );
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document.write( "[ Alternatively, observe that (1') and (2') have the same y-intercept, which occurs at x=0, y=b ]<BR>\n" );
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document.write( "Ans:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+matrix%281%2C+3%2C+%22%28+%22%2C+%220%2C+5%22%2C+%22+%29+%22+%29+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+matrix%281%2C+3%2C+%22%28+%22%2C+%220%2C+5%22%2C+%22+%29+%22+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   is the orthocenter.\r<BR>\n" );
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document.write( "                                                                 </SPAN>\n" );
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