document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=618334>Question 618334</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person standing at the junccction 9CROSSING0 of two sssstraight paths,represented by the equatins 2x -3y +4=0 and 3x +4y +5 =0 wants to reach the path wwwwhose equation is 6x-7y+8=0 in the least time.find the equation of the path that he should follow. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390281 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=390281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person standing at the junccction 9CROSSING0 of two sssstraight paths,represented by the equatins 2x -3y +4=0 and 3x +4y +5 =0 wants to reach the path wwwwhose equation is 6x-7y+8=0 in the least time.find the equation of the path that he should follow.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "find coordinates at junction of first two straight paths:<BR>\n" );
document.write( "2x -3y +4=0<BR>\n" );
document.write( "3x +4y +5 =0<BR>\n" );
document.write( "..<BR>\n" );
document.write( "6x-9y+12=0<BR>\n" );
document.write( "6x+8y+10=0<BR>\n" );
document.write( "subtract<BR>\n" );
document.write( "-17y+2=0<BR>\n" );
document.write( "y=2/17<BR>\n" );
document.write( "..<BR>\n" );
document.write( "8x-12y+16=0<BR>\n" );
document.write( "9x+12y+15=0<BR>\n" );
document.write( "add<BR>\n" );
document.write( "17x+31=0<BR>\n" );
document.write( "x=-31/17<BR>\n" );
document.write( "(x,y) coordinates at junction:(-31/17,2/17)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "slope of path to reach<BR>\n" );
document.write( "6x-7y+8=0<BR>\n" );
document.write( "7y=6x+8<BR>\n" );
document.write( "y=6x/7+8<BR>\n" );
document.write( "slope=6/7<BR>\n" );
document.write( "..<BR>\n" );
document.write( "shortest path would be a perpendicular line from this line to coordinates of the junction<BR>\n" );
document.write( "slope of perpendicular line =-7/6 (negative reciprocal)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "equation: y=-7x/6+b<BR>\n" );
document.write( "solve for b using coordinates of the junction<BR>\n" );
document.write( "2/17=-7*(-31/17)/6+b<BR>\n" );
document.write( "b=2/17+7*(-31/17)/6&#8776;-2<BR>\n" );
document.write( "Equation of path to follow:<BR>\n" );
document.write( "y=-7x/6-2<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-4%2C+4%2C+-4%2C+4%2C2x%2F3%2B4%2F3%2C-3x%2F4-5%2F4%2C6x%2F7%2B8%2F7%2C-7x%2F6-2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );