What Are Rotations, in Geometry?

Rotations spin a figure around a point

In geometry, rotation means spinning something around a specific point. This can be one of the shape's corners, a point inside the shape, or even a point outside the shape. When we talk about rotation, we need to specify two things:

1. What point the shape is rotating around.
2. How much the shape is rotating (in degrees or radians).

In the image below, the shape on the left rotates $90^\circ$ clockwise around the green point $(-0.5, 0)$, resulting in the shape on the right. The original red vertex $(-1.25,1)$ is rotated to its new location, $(0.5,0.75)$.