Question

Which of the following is an equivalent transformation to rotation of an object clockwise 90 degrees?(1 point)
Responses

rotation about the origin of 180 degrees counterclockwise
rotation about the origin of 180 degrees counterclockwise

rotation about the origin of 90 degrees counterclockwise
rotation about the origin of 90 degrees counterclockwise

rotation about the origin of 270 degrees counterclockwise
rotation about the origin of 270 degrees counterclockwise

rotation about the origin of 270 degrees clockwise

Answer 1

To determine which transformation is equivalent to a clockwise rotation of 90 degrees, we can analyze each option provided:

1. **Rotation about the origin of 180 degrees counterclockwise** - This is not equivalent as it results in a half-turn, producing a 180-degree rotation in the opposite direction.

2. **Rotation about the origin of 90 degrees counterclockwise** - This is the opposite of a 90-degree clockwise rotation, resulting in a counterclockwise turn.

3. **Rotation about the origin of 270 degrees counterclockwise** - A counterclockwise rotation of 270 degrees is equivalent to a clockwise rotation of 90 degrees (because 360 - 270 = 90).

4. **Rotation about the origin of 270 degrees clockwise** - This is the same as a counterclockwise rotation of 90 degrees, hence, 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.**