To determine which transformation is equivalent to a clockwise rotation of 90 degrees, we can analyze the options provided.
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Rotation about the origin of 90 degrees counterclockwise: This is equivalent to rotating the object in the opposite direction (counterclockwise), so it is not equivalent.
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Rotation about the origin of 180 degrees counterclockwise: A 180-degree rotation flips the object to the opposite direction but does not achieve the same result as a 90-degree rotation, so it is not equivalent.
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Rotation about the origin of 270 degrees counterclockwise: A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. This is because rotating 270 degrees counterclockwise is the same as removing 180 degrees (which places the object backwards) and then an additional 90 degrees to the left.
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Rotation about the origin of 270 degrees clockwise: This would indeed rotate the object 270 degrees in the clockwise direction, which is not equivalent to a 90-degree clockwise rotation.
Therefore, the equivalent transformation to a clockwise rotation of 90 degrees is:
Rotation about the origin of 270 degrees counterclockwise.