This is a good question. There is a subtle, relational difference I see working here.
If the points will all wind up in different places, you would say you are changing the locations of the points. Say you have three points, one at 0,1 on a graph, one at 0,2 and one at 0,3. You move them so that the locations are 1,1 and 2,2 and 3,3, respectively. Each location has changed, so all the locations have changed.
If the points were all located within one area, and the location of the area changed while the points in the aggregate remained in the same place with respect to each other, you could say the location of the points changed. This could be true if, say, the points formed, say, an equilateral triangle inside a square whose lower left corner was situated at location 0,0 on a graph. The square is moved to location 1,1. That would warrant use of the singular. Note that the locations of the points also change with respect to the larger domain, but not the smaller one. It would be like moving a piece of paper (the smaller domain) with points on it from one location to the other within the larger domain (the graph).
The difference depends on which you are trying to emphasize.