# SOLUTION: 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+

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 Click here to see ALL problems on Length-and-distance Question 618334: 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.Answer by lwsshak3(6481)   (Show Source): You can put this solution on YOUR website!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. ** find coordinates at junction of first two straight paths: 2x -3y +4=0 3x +4y +5 =0 .. 6x-9y+12=0 6x+8y+10=0 subtract -17y+2=0 y=2/17 .. 8x-12y+16=0 9x+12y+15=0 add 17x+31=0 x=-31/17 (x,y) coordinates at junction:(-31/17,2/17) .. slope of path to reach 6x-7y+8=0 7y=6x+8 y=6x/7+8 slope=6/7 .. shortest path would be a perpendicular line from this line to coordinates of the junction slope of perpendicular line =-7/6 (negative reciprocal) .. equation: y=-7x/6+b solve for b using coordinates of the junction 2/17=-7*(-31/17)/6+b b=2/17+7*(-31/17)/6≈-2 Equation of path to follow: y=-7x/6-2 see graph below: