To ease your problem, consider "L" as you x-axis
Then the coordinate become:
A(- 4 , 3) and B(1 , 2) [you notice that just the y's changed]
This is a reflection problem.
Reflect point B across the river line "L" to get B', symmetric of B about L.
The coordinates of B'(1 , -1) [remember L is our new x-axis]
JOIN A to B' . AB' intersect L, say in H
We have to find the shortest way such that AH + HB = shortest.
But HB = HB' (symmetry about L) , then I can write instead of
AH + HB →→ AH + HB'. This is the shortest since the shortest distance between 2 points is the straight line and H is the point requiered