The equations of the given lines are
2x – 3y + 4 = 0 …………………. (1)
3x + 4y – 5 = 0 …………………. (2)
6x – 7y + 8 = 0 ……………….… (3)
The person is standing at the junction of the paths represented by lines (1) and (2).
On solving equations (1) and (2), we obtain .x = -1/17 and y = 22/17.
Thus, the person is standing at point ( - 1/17 , 22/17)
The person can reach path (3) in the least time if he walks along the perpendicular line
to (3) from point ( - 1/17 , 22/17)
