Crossing a river?

Question

If you have to build a bridge, which can only be perpendicular to the river banks, where would you build it in order to make the shortest path from point 1 on one side to point 2 on the other? Points 1 & 2 can be anywhere on each respective side.

To give a picture - say on a graph, point 1 is at (2,1), point 2 is at (7,5). The river is between the 2 lines at y=3 and y=4. But the pionts can be anywhere, and the river can be any width between the 2 points.

Answer 1

You answered your question - assume the banks are parallel (the river is not getting wider or narrower - pick a point on one side. Construct a perpendicular to the bank and where that line hits the other bank is the other point. It also happens that with parallel banks, the shortest distance is perpendicular to the bank.