document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=907680>Question 907680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a number t such that the distance between (-2,2)  and (3t,2t) is as small as possible. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #550542 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=550542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the distance formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=%28-2-3t%29%5E2%2B%282-2t%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%28-2-3t%29%5E2%2B%282-2t%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=%289t%5E2%2B12t%2B4%29%2B%284t%5E2-8t%2B4%29 ALIGN=MIDDLE  ALT=\"D%5E2=%289t%5E2%2B12t%2B4%29%2B%284t%5E2-8t%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=13t%5E2%2B4t%2B8 ALIGN=MIDDLE  ALT=\"D%5E2=13t%5E2%2B4t%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To minimize the distance squared, take the derivative of the distance squared and set it equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28D%5E2%29%2Fdt=26t%2B4%7D%7D%0D%0A%7B%7B%7B26t%2B4=0 ALIGN=MIDDLE  ALT=\"d%28D%5E2%29%2Fdt=26t%2B4%7D%7D%0D%0A%7B%7B%7B26t%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26t=-4 ALIGN=MIDDLE  ALT=\"26t=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-4%2F26 ALIGN=MIDDLE  ALT=\"t=-4%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2%2F13 ALIGN=MIDDLE  ALT=\"t=-2%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-3%2C3%2C-3%2C3%2Cgrid%281%29%2Ccircle%28-2%2C2%2C0.2%29%2Ccircle%28-6%2F13%2C-4%2F13%2C0.2%29%2Cblue%28line%28-2%2C2%2C-6%2F13%2C-4%2F13%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( "You could also do it geometrically.<BR>\n" );
document.write( "(3t,2t) defines a line through the origin where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F3%29x ALIGN=MIDDLE  ALT=\"y=%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You could find the line perpendicular to that line through the point (-2,2).<BR>\n" );
document.write( "Perpendicular lines have negative reciprocal slopes so the slope would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3%2F2 ALIGN=MIDDLE  ALT=\"m=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the point slope form of a line,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-2=-%283%2F2%29%28x-%28-2%29%29 ALIGN=MIDDLE  ALT=\"y-2=-%283%2F2%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-2=-%283%2F2%29x-3 ALIGN=MIDDLE  ALT=\"y-2=-%283%2F2%29x-3\"   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-1 ALIGN=MIDDLE  ALT=\"y=-%283%2F2%29x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then finding the intersection of the two lines, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x=-%283%2F2%29x-1 ALIGN=MIDDLE  ALT=\"%282%2F3%29x=-%283%2F2%29x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%282%2F3%2B3%2F2%29=-1 ALIGN=MIDDLE  ALT=\"x%282%2F3%2B3%2F2%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2813%2F6%29=-1 ALIGN=MIDDLE  ALT=\"x%2813%2F6%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6%2F13 ALIGN=MIDDLE  ALT=\"x=-6%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3t=-6%2F13 ALIGN=MIDDLE  ALT=\"3t=-6%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2%2F13 ALIGN=MIDDLE  ALT=\"t=-2%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-3%2C3%2C-3%2C3%2Cgrid%281%29%2Ccircle%28-2%2C2%2C0.2%29%2Ccircle%28-6%2F13%2C-4%2F13%2C0.2%29%2Ccircle%28-6%2F13%2C-4%2F13%2C0.2%29%2Cgraph%28300%2C300%2C-3%2C3%2C-3%2C3%2C%282%2F3%29x%2C-%283%2F2%29x-1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );