4.4 Equidistant Theorem

Interact with the applet below for a few minutes. Then answer the questions that follow. Be sure to alter the locations of points A, B, and C each time before (and even after) you re-slide the slider!

How would you describe the blue line p with respect to the segment with endpoints A and B? What exactly is line p?

Notice how point C always stays on line p. What can you conclude about the distances AC and BC?

Formally prove, (in the format of a 2-column proof, paragraph proof, or coordinate-geometry proof), that your conclusion for (2) is true for any point C that lies on line p.