To determine which transformation is equivalent to a clockwise rotation of 90 degrees, we can analyze the provided options in terms of their rotations:
-
Rotation about the origin of 270 degrees counterclockwise:
- A clockwise rotation of 90 degrees is equivalent to a counterclockwise rotation of 270 degrees (since \(360^\circ - 90^\circ = 270^\circ\)).
- This option is equivalent.
-
Rotation about the origin of 90 degrees counterclockwise:
- This rotation is not equivalent; it rotates the object 90 degrees in the opposite direction.
- This option is not equivalent.
-
Rotation about the origin of 270 degrees clockwise:
- A clockwise rotation of 270 degrees is the same as a counterclockwise rotation of 90 degrees (since \(360^\circ - 270^\circ = 90^\circ\)).
- This option is not equivalent.
-
Rotation about the origin of 180 degrees counterclockwise:
- A rotation of 180 degrees does not result in the same orientation as a 90-degree clockwise rotation.
- This option is not equivalent.
Thus, the equivalent transformation to a clockwise rotation of 90 degrees is the rotation about the origin of 270 degrees counterclockwise.