If that sounds a little technical, don't worry—the following example will make everything clear!

To find the locus of all points equidistant from two given points, follow these steps:

**Identify a pattern.**The figure shows the two given points,*A*and*B,*along with four new points that are each equidistant from the given points.Do you see the pattern? You got it—it's a vertical line that goes through the midpoint of the segment that connects the two given points. In other words, it's that segment's perpendicular bisector.

**Look outside the pattern.**You come up empty in Step 2. Check any point*not*on the perpendicular bisector of line*AB*, and you see that it's*not*equidistant from*A*and*B.*Thus, you have no points to add.**Look inside the pattern.**Nothing noteworthy here, either. Every point on the perpendicular bisector of line*AB*is, in fact, equidistant from*A*and*B.*Thus, no points should be excluded. (Warning: Don't allow yourself to get a bit lazy and skip Steps 2 and 3!)**Draw the locus and describe it in words.**This figure shows the locus, and the caption gives its description.