[color=#000000]Interact with the applet below for a few minutes. Then answer the questions that follow. [br][i]Be sure to alter the locations of points A, B, and C each time before (and even after) you re-slide the slider! [/i] [br][/color]

[b]Questions:[br][br][/b][color=#000000]1) How would you describe both the [/color][b][color=#1e84cc]blue line p[/color] [/b]and the [b][color=#6aa84f]green line k[/color][/b] [color=#000000]with respect to the [/color][b]segment with endpoints [i]A[/i] and [i]B[/i][/b][color=#000000]? (Hint: Check when slider is half way)[br][br]2) Therefore, we can say point [i]D[/i] is _______________ from points A and B. [/color][br][br]3) [i]C [/i]is a point on the [b][color=#1e84cc]blue [/color][/b][color=#1e84cc][b]line [/b][b]p[/b][/color][color=#000000]. What can you conclude about the [/color][b]distances [i][color=#ff0000]AC[/color][/i][/b][color=#000000] and [/color][i][color=#cc0000][b]BC[/b][/color][/i][color=#000000]? (Hint: Finish sliding the slider)[br][/color][br]4) Now how would you describe the [b][color=#1e84cc]blue line p[/color][/b]? (Hint: This should be different than #1)[color=#000000]5) Formally prove, (in the format of a 2-column proof), that your conclusion form #4 is true for any set of [/color]points[color=#000000] that are equidistant from A and B. [br][br][/color]5) Now take a look at the distances FA and FB, when point F is not contained by the [color=#1e84cc][b]blue line p[/b][/color]. Notice that these distances are not the same, therefore the [color=#6aa84f][b]green line k[/b][/color] is does not form the same special segment as the [color=#1e84cc][b]blue line p[/b][/color].[br] [br]