If you were to describe a rotation of triangle ABC what information would you need to include in your description

You would need to include the center of rotation. For many problems, the center is usually the origin (0,0). This is a default assumed center. Though the center could easily be any other point.

In addition, you also need the amount of rotation that is being applied (eg: 90 degrees).

The last bit of info you need is whether you're going clockwise or counterclockwise. For 180 degree rotations, it doesn't matter, but for everything else it does matter.