Question

A person standing at the junction (crossing) of two straight paths represented by the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he should follow.

Answer 1

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).

The person can reach path (3) in the least time if he walks along the perpendicular line

Hence, the path that the person should follow is 119 x+102y =125