document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131849>Question 1131849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Points B(b,0) and C(c,10) are to be placed on this graph so that the distance from A to B to C to D is a minimum. Find the value of b.<BR>\n" );
document.write( "Note: point A is at (0,4) and point D is at (8,9)'\r<BR>\n" );
document.write( "\n" );
document.write( "I got a hint from my teacher saying to reflect point A on the x axis. I don�t know what to do from there. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748550 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> points B(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and C(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "point A is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and point D is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "slope of AB is :\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%284-0%29%2F%280-b%29=-4%2Fb ALIGN=MIDDLE  ALT=\"m=%284-0%29%2F%280-b%29=-4%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "slope of BC is: \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%2810-0%29%2F%28c-b%29=10%2F%28c-b%29 ALIGN=MIDDLE  ALT=\"m=%2810-0%29%2F%28c-b%29=10%2F%28c-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "slope of CD is :\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%289-10%29%2F%288-c%29=-1%2F%288-c%29 ALIGN=MIDDLE  ALT=\"m=%289-10%29%2F%288-c%29=-1%2F%288-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The minimum distance  from A to B to C to D will be if the slopes of AB and CD are the same and the slope of BC is the opposite.\r<BR>\n" );
document.write( "\n" );
document.write( "The slope of AB is the same as the slope of CD:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2Fb=-1%2F%288-c%29 ALIGN=MIDDLE  ALT=\"-4%2Fb=-1%2F%288-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4c-32=-b ALIGN=MIDDLE  ALT=\"4c-32=-b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4c=32-b ALIGN=MIDDLE  ALT=\"4c=32-b\"   DISABLED_style= \"max-width:90%; height:auto;\" >............... (1)\r<BR>\n" );
document.write( "\n" );
document.write( "The slope of BC is the opposite of the slope of AB:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%28c-b%29=4%2Fb ALIGN=MIDDLE  ALT=\"10%2F%28c-b%29=4%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4c-4b=10b ALIGN=MIDDLE  ALT=\"4c-4b=10b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4c=14b ALIGN=MIDDLE  ALT=\"4c=14b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............. (2)\r<BR>\n" );
document.write( "\n" );
document.write( "from (1) and (2):\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32-b=14b ALIGN=MIDDLE  ALT=\"32-b=14b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32=14b%2Bb ALIGN=MIDDLE  ALT=\"32=14b%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15b=32 ALIGN=MIDDLE  ALT=\"15b=32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=32%2F15 ALIGN=MIDDLE  ALT=\"b=32%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2%26+2%2F15 ALIGN=MIDDLE  ALT=\"b=2%26+2%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );