[color=#000000]In the applet below, note that[/color] [color=#ff00ff]point [i]C[/i][/color] [color=#38761d]is equidistant[/color][color=#000000] from [i]A[/i] and [i]B[/i].  [br]In this applet,[/color] [b][i][color=#ff00ff]C[/color][/i] [color=#000000]will [/color][color=#38761d]ALWAYS REMAIN EQUIDISTANT[/color] [color=#000000]from [i]A[/i] and [i]B[/i].[/color][/b] [br][color=#000000]Also note that [i]A[/i] and [i]B[/i] serve as endpoints of a segment.  [/color][br][br][color=#ff0000][b]Directions:[/b][/color][br][br][color=#000000]1) Drag [/color][i][color=#ff00ff]C[/color][/i][color=#000000] around as much as you'd like (without moving [i]A[/i] and [i]B[/i]).[/color][br][color=#000000]    What can you conclude about the locus (set of points) in the plane[/color][br][color=#000000]    that are equidistant from the endpoints of a segment?[/color][br][color=#000000]    What does this locus look like?  [/color][br][br][color=#000000]2) Let's test this conjecture again. [/color][br][color=#000000]    Change the location of point [i]A[/i] and point [i]B[/i].  [/color][br][color=#000000]    Hit the "Clear Trace" button to erase the previous traces of point [/color][i][color=#ff00ff]C[/color][/i][color=#000000].  [/color][br][color=#000000]    Repeat Step 1.  [/color][br][br][color=#000000]3) Use the tools of GeoGebra to now show that your conjecture is true.  [/color]