Two cities are form different sides of a river. A highway connecting A and B needs to be built so that part of the highway is on a bridge XY perpendicular to the parallel banks of the river. Where should the bridge be built so that AXYB is as short as possible.
I believe that I could project YB up so that X and Y coincide. Then by connecting point A to B', I would take the new intersection point of this line and the bank of the river. This point would be one of the locations where the bridge should be built so that AXYB is as short as possible. I just don't know how to put all this into mathematical terms.
Best Answer
We assume that the banks of the river are parallel.
From city A, draw a line AA’ that is equal and parallel to the width of the river. Such an act can successfully “virtually move” city A to location A’.
The shortest distance between the 2 cities is now A’B (the green line).
This line somehow will cut the river bank at Y.
From Y, build the perpendicular bridge YX.
The highway is now AX + XY + YB.