Question

What is the maximal distance between two points \(A, B \in [\Delta x, \Delta y]\) as they evolve with time? See link.

Answer 1

http://i.imgur.com/mGIsoEp.png is the image.

Answer 2

http://i.imgur.com/StlxZVu.jpg is the mentioned graphic resource.

Answer 3

For whatever it is worth, here is my post on Stack Exchange: http://math.stackexchange.com/questions/542201/what-is-the-maximal-distance-between-two-points-a-b-in-delta-x-delta-y
"NOTE: The actual problem is 3-dimensional. The way I describe it is 2-dimensional."