[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][/color]
[color=#000000]How would you describe the [/color][color=#1e84cc][b]blue line p [/b][/color][color=#000000]with respect to the [/color][b]segment with endpoints [i]A[/i] and [i]B[/i][/b][color=#000000]? What exactly is [/color][b][color=#1e84cc]line p[/color][/b][color=#000000]? [/color]
[color=#000000]Notice how point [/color][i][color=#000000]C[/color][/i][color=#000000] always stays on [/color][color=#1e84cc][b]line [/b][b]p[/b][/color][color=#000000]. What can you conclude about the [/color][color=#cc0000][b]distances [i]AC[/i][/b][/color][color=#000000] and [/color][i][color=#cc0000][b]BC[/b][/color][/i][color=#000000]?[/color]
[color=#000000]Formally prove, (in the format of a 2-column proof, paragraph proof, or coordinate-geometry proof), that your conclusion for (2) is true for [i]any point [/i][i]C[/i] that lies on [/color][color=#1e84cc][b]line p[/b][/color][color=#000000]. [/color]