Quick Locus Exploration

In the app below, line i is said to be the perpendicular bisector of . What does it means for a line to be a perpendicular bisector of a segment? (Google it if you can't remember.)

Interact with this construction for a bit. Then answer the question that follows. (Points D and F are moveable).

What can we conclude about segments and ? Why can we conclude this?

Drag point D along line d below. What do you notice? You can clear traces and readjust the positions of F and line d at any time.

Given your response to the previous questions and given what you see in the app above, how would you describe the locus (set) of points (or possible locations for point P)? What's so special about them? Describe.