Rotation of 0-360 degrees around a centre (NJT)

What stays the [b]same[/b] and what [b]changes[/b] when you move [list] [*]the slider? [*]the vertices B,C and D? [*]the centre of rotation? [/list] Are there any points that do not move under this transformation?

[color=#0a971e]Created by N.Trubridge[/color]