document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=601037>Question 601037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the base of a triangle is given by the co-ordinates of the end points (0,0), (0,6). If the slopes of the other two sides are 2 and - 2/3, determine the co-ordinates of the third vertex.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379576 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=379576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Actually, the third vertex can be in one of two places.  If the slope 2 line goes through (0,6) and the slope <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{2}{3}\"> line goes through (0,0) you have one case.  If the lines are reversed you have another case.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case 1:  slope 2 line through (0,6).  Equation of this line: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ 2x\ +\ 6\"> (Slope-intercept form.)  Slope <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{2}{3}\"> line through (0,0).  Equation of this line:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\ =\ -\frac{2}{3}x\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve the system of equations:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left{y\ =\ 2x\ +\ 6\cr y\ =\ -\frac{2}{3}x\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x,\,y)\"> which is the point of intersection of the two lines.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The other case has the following system of equations:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left{y\ =\ 2x\cr y\ =\ -\frac{2}{3}x\ +\ 6\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28%0D%0A500%2C+500%2C+-5%2C5%2C-2%2C8%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28%0D%0A500%2C+500%2C+-5%2C5%2C-2%2C8%2C%0D%0A2x%2B6%2C%28-2%2F3%29x%2C%28-2%2F3%29x%2B6%2C2x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<div  DISABLED_style= \"text-align:center\"><a  rel=nofollow HREF=\"http://outcampaign.org/\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png\" border=\"0\" alt=\"The Out Campaign: Scarlet Letter of Atheism\" width=\"143\" height=\"122\" /></a></div><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );