In example 3 on pages 573 and 574, you were examining the locus of points equidistant from two given points. We will investigate the locus below.
In the sketch below are three points A, B and P. Notice that as you move P the distance between P and the two other points is the same, that is, PA = PB. Can you spot any relationship between the path of P and the two points A and B? P may be traced by clicking on the Trace button. At any point, after you have started tracing, you may erase the traced points by clicking on the red X in the bottom right corner of the screen. Once you think you have the relationship, move A and B to new positions and see if your conjecture holds for this new arrangement.
The sketch on this page was created with a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work were funded by the National Science Foundation (awards DMI 9561674 & 9623018).