How A

Reflect the point $$$(x_2, y_2)$$$ "across" the river, ie. replace with $$$(x_2, -y_2).$$$ If you pick a point $$$p$$$ on the river to go to then distance from $$$p$$$ to $$$(x_2,y_2)$$$ is the same as distance from $$$p$$$ to $$$(x_2,-y_2).$$$ Then by triangle inequality (shortest distance between two points in the plane is the straight line segment between them), so you just choose $$$p$$$ so that $$$(x_1,y_1),p,(x_2,-y_2)$$$ are collinear and the minimum distance is just the distance between $$$(x_1,y_1)$$$ and $$$(x_2,-y_2).$$$