# 4.4 Equidistant Theorem

- Author:
- elishevacarl, Tim Brzezinski

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**.