Which of the following is an equivalent transformation to rotation of an object clockwise 90 degrees?

Question

1. rotation about the origin of 90 degrees counterclockwise
2. rotation about the origin of 270 degrees clockwise
3. rotation about the origin of 180 degrees counterclockwise
4. rotation about the origin of 270 degrees counterclockwise

Answer 1

To determine which transformations are equivalent to a clockwise rotation of 90 degrees, we can analyze each option.

1. Rotation about the origin of 90 degrees counterclockwise: This is equivalent to a clockwise rotation of 270 degrees. This is not equivalent to a 90-degree clockwise rotation.

2. Rotation about the origin of 270 degrees clockwise: A clockwise rotation of 270 degrees is equivalent to a counterclockwise rotation of 90 degrees, thus this transformation is equivalent to a clockwise rotation of 90 degrees. This option is equivalent.

3. Rotation about the origin of 180 degrees counterclockwise: This transformation changes the object's position by flipping it around the origin, which does not yield the same position as a 90-degree clockwise rotation. This option is not equivalent.

4. Rotation about the origin of 270 degrees counterclockwise: This is equivalent to a clockwise rotation of 90 degrees (as noted earlier). Hence, this option is also equivalent.

So, the correct answers are 2 and 4:

• 2. rotation about the origin of 270 degrees clockwise
• 4. rotation about the origin of 270 degrees counterclockwise