document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118344>Question 118344</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me to solve this problem: Given the points P(-1,-2) Q(4,2) and R(1,m) in the coordinate plane. find the value of m so that PR + PQ is minimum.<BR>\n" );
document.write( "thanks!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86463 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=86463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the points P(-1,-2) Q(4,2) and R(1,m) in the coordinate plane. find the value of m so that PR + PQ is minimum.<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "PR = sqrt[(m+2)^2+(1+1)^2] = sqrt[m^2+2m+5]<BR>\n" );
document.write( "PQ = sqrt[(2+2)^2+(4+1)^2] = sqrt[41]<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "PR + PQ = sqrt[m^2+2m+5] + sqrt[41]<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "To minimize the sum we need to minimize m^2+2m+5:<BR>\n" );
document.write( "That occurs when m = -b/2a = -2/2 = -1<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );