Math Forum :: View topic – 2 points moving on a graph

Let A and B be two points with the same “y” coordinates in the orthogonal system of coordinates Oxy. Let’s imagine that there’s a graph of some linear broken function (a polyline) such that no point of this graph has smaller “y” coordinate than points A,B and this polyline starts in A and ends in B. Then in the same moment from both points A, B two dots start to move (not always against each other) so that they would always have the same “y” coordinate. Prove that they can meet.

It’s easy to see that the meeting point should be the point with the higher “y” coordinate (or in case that there are more points with this property, any arbitrary one of them). But if we try to solve some cases of the task, we can easily lose in it… It’s necessary to take it with bird’s eye view that I still miss. Thanks.