document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=700643>Question 700643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find out how to find the orthocenter with the given vertices of M(-5,0), N (0,14) O(0,0)  I already graphed it.  I don't know HOW to find the orthocenter of a triangle, or what an orthocenter even is.  Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #431927 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=431927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The orthocenter is the intersection of the altitudes.\r<BR>\n" );
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document.write( "Since you have a right triangle, use the fact that all right triangles have an orthocenter coincident with the right angle vertex.  (Because the two legs <i>are</i> altitudes.)\r<BR>\n" );
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document.write( "In general though, you would:\r<BR>\n" );
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document.write( "1.  Use the slope formula determine the slope of one side of the triangle.\r<BR>\n" );
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document.write( "2.  Use the point-slope form and the fact that perpendicular lines have negative reciprocal slopes to write an equation of a line perpendicular to side chosen for step 1 that passes through the not-included vertex.\r<BR>\n" );
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document.write( "3.  Repeat steps 1 and 2 for one of the other sides.\r<BR>\n" );
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document.write( "4.  Solve the system of equations consisting of the equations derived in steps 2 and 3.  The solution set will be the orthocenter.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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