document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=974087>Question 974087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this:\r<BR>\n" );
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document.write( "Find a number t such that the distance between <BR>\n" );
document.write( "(&#8722;3, 2)<BR>\n" );
document.write( " and <BR>\n" );
document.write( "(3t, 2t)<BR>\n" );
document.write( " 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 #596103 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=596103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (-3,2) and (3t,2t)\r<BR>\n" );
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document.write( "need to minimize the squared deviations of (2t-2)^2 and (3t+3)^2 \r<BR>\n" );
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document.write( "Take the first derivative and set it equal to zero.\r<BR>\n" );
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document.write( "2(2t-2)*2 + 2(3t+3)*3=0\r<BR>\n" );
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document.write( "8t-16 + 18t +18=0\r<BR>\n" );
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document.write( "26t+2=0<BR>\n" );
document.write( "t=(-1/13)\r<BR>\n" );
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document.write( "(-3,2), (-3/13,-2/13)\r<BR>\n" );
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document.write( "Distance is sqrt [(36/13)^2) + (28/13)^2 ]=sqrt (7.67+ 4.64)=3.51 units\r<BR>\n" );
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document.write( "Try 0 for t<BR>\n" );
document.write( "(-3,2) and (0,0)  ;;; distance sqrt (13)=3.61\r<BR>\n" );
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document.write( "The graph shows the line that the two points are on.  The curve is the distance between the two points for various values of t.  It is a minimum at (-2/13) for t.  The distance from that minimum to the line is minimized.\r<BR>\n" );
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