Explore the rotation of triangle ABC to its image A'B'C' about the origin. Use the slider to change the angle of rotation and drag the vertices of ABC. Your goal is to discover how rotation transforms the triangle and derive the coordinate rules.
[list][*]Drag a vertex of [b]ABC[/b]. What happens to [b]A'B'C'[/b]? What measurements (side lengths, angles) remain unchanged?[/*][/list]
[list][*]Set the rotation angle to [b]90°[/b]. How are the positions of [b]ABC[/b] and [b]A'B'C'[/b] related? What about at [b]180°[/b] and [b]270°[/b]?[/*][/list]
[list][*]For a vertex [b]A[/b] and its image [b]A'[/b], what is the relationship between their distances from the origin? What about the angle formed by [b]A[/b], the origin, and [b]A'[/b]?[/*][/list]
[list][*]With a [b]90°[/b] rotation, if point [b]A[/b] is at [b](x, y)[/b], what are the coordinates of [b]A'[/b]? Derive similar rules for [b]180°[/b] and [b]270°[/b].[/*][/list]
[list][*]How would rotating by [b]-90°[/b] compare to rotating by [b]270°[/b]? What happens after a full [b]360°[/b]rotation?[/*][/list]
[list][*]In your own words, describe what information is needed to completely define a rotation.[/*][/list]