document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175131>Question 175131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with the following<BR>\n" );
document.write( "- Find the shortest distance from the point (3,1) to the line 3x+y=-2 to the nearest tenth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130207 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=130207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need help with the following<BR>\n" );
document.write( "- Find the shortest distance from the point (3,1) to the line 3x+y=-2 to the nearest tenth.<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Draw the picture.<BR>\n" );
document.write( "Find the equation of the line perpendicular to the given line and passing<BR>\n" );
document.write( "thru (3,1)<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "slope of the given line: -3<BR>\n" );
document.write( "slope of the perpendicular line: 1/3<BR>\n" );
document.write( "intercept for this line: 1 = (1/3)3 + b<BR>\n" );
document.write( "b = 0<BR>\n" );
document.write( "Equation of the perpendicular line: y = (1/3)x<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "intercept of the given line and the perpendicular line:<BR>\n" );
document.write( "y = (1/3)x<BR>\n" );
document.write( "y = -3x-2<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Substitute to solve for \"x\": (1/3)x = -3x-2 ; (8/3)x=-2;x =-3/4<BR>\n" );
document.write( "Since y = (1/3)x y = (1/3)(-3/4) = -1/4<BR>\n" );
document.write( "------<BR>\n" );
document.write( "So the intercept point is (-3/4,1/4)<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Find the distance from (-3/4,-1/4) t0 (3,1)<BR>\n" );
document.write( "distance = sqrt[(1--1/4)^2 + (3--3/4)^2] = sqrt[(25/16) + (225/16)]<BR>\n" );
document.write( "= sqrt[250/16] = (5/4)sqrt(10)<BR>\n" );
document.write( "============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );