document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=934028>Question 934028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is orthocenter of points A(0,10) B(4,10) C(-2,4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568100 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=568100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C10%2C-2%2C12%2Cgrid%281%29%2Ccircle%280%2C10%2C0.4%29%2Ccircle%284%2C10%2C0.4%29%2Ccircle%28-2%2C4%2C0.4%29%2C%0D%0Aline%280%2C10%2C4%2C10%29%2Cline%284%2C10%2C-2%2C4%29%2Cline%28-2%2C4%2C0%2C10%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the midpoints. <BR>\n" );
document.write( "Midpoint of AB : (2,10)<BR>\n" );
document.write( "Midpoint of BC : <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BBC%5D=%284-2%29%2F2=1 ALIGN=MIDDLE  ALT=\"x%5BBC%5D=%284-2%29%2F2=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%5BBC%5D=%2810%2B4%29%2F2=7 ALIGN=MIDDLE  ALT=\"y%5BBC%5D=%2810%2B4%29%2F2=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Midpoint of AC : <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BAC%5D=%280-2%29%2F2=-1 ALIGN=MIDDLE  ALT=\"x%5BAC%5D=%280-2%29%2F2=-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%5BAC%5D=%2810%2B4%29%2F2=7 ALIGN=MIDDLE  ALT=\"y%5BAC%5D=%2810%2B4%29%2F2=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C10%2C-2%2C12%2Cgrid%281%29%2Ccircle%280%2C10%2C0.4%29%2Ccircle%284%2C10%2C0.4%29%2Ccircle%28-2%2C4%2C0.4%29%2Ccircle%282%2C10%2C0.25%29%2Ccircle%28-1%2C7%2C0.25%29%2Ccircle%281%2C7%2C0.25%29%2C%0D%0Aline%280%2C10%2C4%2C10%29%2Cline%284%2C10%2C-2%2C4%29%2Cline%28-2%2C4%2C0%2C10%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the diagram, it looks like the orthocenter will be (0,7).<BR>\n" );
document.write( "We definitely know that from the midpoint of BC to the midpoint of AC, the equation of the line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7 ALIGN=MIDDLE  ALT=\"y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The line from C to the midpoint of AB is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=%28%284-10%29%2F%28-2-2%29%29%28x-%28-2%29%29 ALIGN=MIDDLE  ALT=\"y-4=%28%284-10%29%2F%28-2-2%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-4=%283%2F2%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"y-4=%283%2F2%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%2F2%29x%2B3 ALIGN=MIDDLE  ALT=\"y-4=%283%2F2%29x%2B3\"   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%2F2%29x%2B7 ALIGN=MIDDLE  ALT=\"y=%283%2F2%29x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since we already know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7 ALIGN=MIDDLE  ALT=\"y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=%283%2F2%29x%2B7 ALIGN=MIDDLE  ALT=\"7=%283%2F2%29x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29x=0 ALIGN=MIDDLE  ALT=\"%283%2F2%29x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(0,7)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C10%2C-2%2C12%2Cgrid%281%29%2Ccircle%280%2C10%2C0.4%29%2Ccircle%284%2C10%2C0.4%29%2Ccircle%28-2%2C4%2C0.4%29%2Ccircle%280%2C7%2C0.1%29%2Ccircle%280%2C7%2C0.15%29%2Ccircle%280%2C7%2C0.2%29%2Ccircle%280%2C7%2C0.25%29%2Ccircle%282%2C10%2C0.25%29%2Ccircle%28-1%2C7%2C0.25%29%2Ccircle%281%2C7%2C0.25%29%2C%0D%0Aline%280%2C10%2C4%2C10%29%2Cline%284%2C10%2C-2%2C4%29%2Cline%28-2%2C4%2C0%2C10%29%2C%0D%0Ablue%28line%28-2%2C4%2C2%2C10%29%29%2C%0D%0Ablue%28line%28-1%2C7%2C1%2C7%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );