Question
Which are properties of rotations? Check all that apply.
Rotations are always counterclockwise.
Rotations preserve size.
Rotations of 360° map a figure to itself.
Lines connecting corresponding points on the pre-image and image are parallel.
Lines connecting corresponding points on the pre-image and image have equal length.
Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.
Rotations are always counterclockwise.
Rotations preserve size.
Rotations of 360° map a figure to itself.
Lines connecting corresponding points on the pre-image and image are parallel.
Lines connecting corresponding points on the pre-image and image have equal length.
Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.
Answers
GPT-4o mini
The properties of rotations include the following:
1. **Rotations are always counterclockwise.** - This statement is **False.** Rotations can be clockwise or counterclockwise; the direction is determined by the specified angle of rotation.
2. **Rotations preserve size.** - This statement is **True.** Rotations maintain the size and shape of the figure being rotated.
3. **Rotations of 360° map a figure to itself.** - This statement is **True.** A rotation of 360° results in the figure being in the same position as it was initially.
4. **Lines connecting corresponding points on the pre-image and image are parallel.** - This statement is **False.** The lines connecting corresponding points may not be parallel; they depend on the angle of rotation.
5. **Lines connecting corresponding points on the pre-image and image have equal length.** - This statement is **True.** The distance between corresponding points in the pre-image and image remains the same after rotation.
6. **Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.** - This statement is **True.** The distance from the center of rotation to a point in the pre-image and the corresponding point in the image is the same.
Based on this assessment, the properties of rotations that apply are:
- Rotations preserve size.
- Rotations of 360° map a figure to itself.
- Lines connecting corresponding points on the pre-image and image have equal length.
- Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.
1. **Rotations are always counterclockwise.** - This statement is **False.** Rotations can be clockwise or counterclockwise; the direction is determined by the specified angle of rotation.
2. **Rotations preserve size.** - This statement is **True.** Rotations maintain the size and shape of the figure being rotated.
3. **Rotations of 360° map a figure to itself.** - This statement is **True.** A rotation of 360° results in the figure being in the same position as it was initially.
4. **Lines connecting corresponding points on the pre-image and image are parallel.** - This statement is **False.** The lines connecting corresponding points may not be parallel; they depend on the angle of rotation.
5. **Lines connecting corresponding points on the pre-image and image have equal length.** - This statement is **True.** The distance between corresponding points in the pre-image and image remains the same after rotation.
6. **Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.** - This statement is **True.** The distance from the center of rotation to a point in the pre-image and the corresponding point in the image is the same.
Based on this assessment, the properties of rotations that apply are:
- Rotations preserve size.
- Rotations of 360° map a figure to itself.
- Lines connecting corresponding points on the pre-image and image have equal length.
- Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.