document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935410>Question 935410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the point which divides the segment from (-5,-4) to (6,-2) in the ratio 2:3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568626 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=568626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The ratio uses the distance between the given points in five equal parts, and you want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > of this distance from one point to the other point.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Distance Formula!  Unknown point between, (x,y).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Distance between given points, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-2-%28-4%29%29%5E2%2B%286-%28-5%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-2-%28-4%29%29%5E2%2B%286-%28-5%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2B121%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2B121%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28125%29 ALIGN=MIDDLE  ALT=\"sqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%285sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%285sqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Another way to take the rest of this is from (-5,-4) to (x,y) is 2 parts and from (x,y) to (6,-2) is 3 parts.  Still two equations are needed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-%28-5%29%29%5E2%2B%28y-%28-4%29%29%5E2%29=%282%2F5%295%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-%28-5%29%29%5E2%2B%28y-%28-4%29%29%5E2%29=%282%2F5%295%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%2B5%29%5E2%2B%28y%2B4%29%5E2%29=2sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x%2B5%29%5E2%2B%28y%2B4%29%5E2%29=2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28%28x%2B5%29%5E2%2B%28y%2B4%29%5E2=20%29 ALIGN=MIDDLE  ALT=\"highlight_green%28%28x%2B5%29%5E2%2B%28y%2B4%29%5E2=20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "AND\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-6%29%5E2%2B%28x-%28-2%29%29%5E2%29=%283%2F5%295%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-6%29%5E2%2B%28x-%28-2%29%29%5E2%29=%283%2F5%295%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-6%29%5E2%2B%28y%2B2%29%5E2%29=3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-6%29%5E2%2B%28y%2B2%29%5E2%29=3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28%28x-6%29%5E2%2B%28y%2B2%29%5E2=45%29 ALIGN=MIDDLE  ALT=\"highlight_green%28%28x-6%29%5E2%2B%28y%2B2%29%5E2=45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Instead of continuing to try to solve these two simultaneous quadratic equations in two variables, find and use the equation of the line containing the two given points!!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-2-%28-4%29%29%2F%286-%28-5%29%29=2%2F11 ALIGN=MIDDLE  ALT=\"m=%28-2-%28-4%29%29%2F%286-%28-5%29%29=2%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and pick second point,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F11%29x%2B%28-2-%282%2F11%29%2A6%29 ALIGN=MIDDLE  ALT=\"y=%282%2F11%29x%2B%28-2-%282%2F11%29%2A6%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=%282%2F11%29x%2B%28-2-12%2F11%29 ALIGN=MIDDLE  ALT=\"y=%282%2F11%29x%2B%28-2-12%2F11%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=%282%2F11%29x%2B%28-22%2F11-12%2F11%29 ALIGN=MIDDLE  ALT=\"y=%282%2F11%29x%2B%28-22%2F11-12%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=%282%2F11%29x-34%2F11%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=%282%2F11%29x-34%2F11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A large number of more arithmetic steps using some substitutions with this line equation.  (unfinished here) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );