Locus #3

The diagram below shows line AB, drawn in blue.[br][br]Locate point C. Drag point C around the screen until it's 2.5 units from line AB.[br]Then, do the same thing with the other red points (D, E, F, G, and H).
Now, points C, D, E, F, G, and H are now all 2.5 units from line AB. If we connected all of these points, what would it look like?
In the diagram below, line AB is shown in blue. Points C and D are not on line AB. The slider controls how far points C and D are from line AB.[br][list][*]Adjust the slider. Notice that C and D move toward or away from the line, depending on how you move the slider.[/*][*]Set your slider to 3 (or as close as you can get it). Now, points C and D are both 3 units from line AB.[/*][*]Move points C and D around the screen. Notice that the distance from each point to the line doesn't change, even when the points move.[/*][/list]
Right click on points C and D and turn the "trace" on. Drag points C and D around the screen to show the locus of the points that are 3 units away from line AB.[br][br]What does the locus look like?
How would the locus change if the slider was set to a different number?
In the diagram below, the red lines are [b]the locus of points d units from line AB.[br][br][/b][list][*]The slider determines the value of d. Adjust the slider to watch what happens to the locus.[/*][*]Set the slider to 3 (or as close as you can get it). Move point B around the screen to change line AB. Watch what happens to the locus when line AB moves.[br][/*][/list]