How to select a particular point when points overlap?

Ok, gents, thanks or the replies. I must not be explaining the problem well enough. Below are some screenshots to illustrate what I’m talking about. Here is a simple rectangle shape and a curve within it. Each successive screenshot is further zoomed in (see the grid indicator in the upper right). Notice that the three lines converge to a single point in the lower left corner. Notice that, no matter how far in I zoom, the lines are represented exactly the same way, since they converge to the same single point in space.

The problem is this: what if you want to select the endpoint of a particular line (for example, the horizontal line) so that you can move its endpoint. How can you select just the endpoint of the horizontal line? How would you select just the endpoint of the curve? How would you select the endpoint of the vertical line?