Final answer:
The rule for a 270° counter clockwise rotation about the origin is to take a point (x, y) and transform it to the point (y, -x), which is equivalent to rotating the point three quadrants around the plane.
Step-by-step explanation:
The rule for a 270° counter clockwise rotation about the origin is as follows: A point (x, y) when rotated 270° counter clockwise around the origin is transformed to the point (y, -x). Imagine looking down on a merry-go-round, for example. As it rotates counterclockwise, a point starting at the right would move to the top, a point at the top would go to the left, a point on the left moves to the bottom, and a point from the bottom moves to the right, indicating a 270° rotation.
This movement is equivalent to the right-hand rule used in physics, where the thumb points in the direction of the angular velocity and the fingers curl in the direction of the disk's rotation. By using the right-hand rule, we can visualize the rotational direction: If the thumb points up (positive z-direction), the fingers curl in the direction of rotation, which in this case is counterclockwise.
In terms of coordinates, if a point A is at (x, y), after a 270° counter clockwise rotation about the origin, point A will be located at (y, -x). This rotation is sometimes also referred to as a 'rotation by three-quadrants counterclockwise.'