The correct option is A 119x+102y=125
The equation of the given lines are
2x−3y+4=0⋯(i)
3x+4y−5=0⋯(ii)
6x−7y+8=0⋯(iii)
Junction of (i) and (ii), solving both the equations, we get
x=−117,y=2217
Thus, the person is standing at
(−117,2217)
The person can reach the path (iii) in the least time if he walks along the perpendicular line to (iii) from the junction point.
Now, line perpendicular to (iii) is
7x+6y+λ=0
Putting (−117,2217), we get
−7+132+17λ17=0⇒λ=−12517
Therefore, the equation of line is
7x+6y−12517=0⇒119x+102y=125