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+

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(11628) (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:

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