Perpendicular Bisector of a Triangle

In the applet below, the perpendicular bisector of segment AB is shown. Interact with this applet for a couple of minutes, making sure to move the 3 BIG MOVEABLE POINTS around. Then, answer the questions that follow.

1.

What can you conclude about any point that lies on the perpendicular bisector of a segment? Hint: What did you notice about the purple point no matter where you put it?