Question

180 degrees rotations practice

Answer 1

Practicing 180-degree rotations involves understanding how points and shapes move in the coordinate plane when rotated around a pivot point, usually the origin (0, 0). A 180-degree rotation results in each point (x, y) transforming to (-x, -y). Here are some practice problems along with their solutions:

### Practice Problems

1. Rotate the point A(3, 4) 180 degrees about the origin.
2. Rotate the point B(-2, 5) 180 degrees about the origin.
3. Rotate the triangle with vertices C(1, 1), D(3, 1), and E(2, 4) 180 degrees about the origin.
4. Rotate the point F(-7, -3) 180 degrees about the origin.
5. Rotate the point G(0, -5) 180 degrees about the origin.

### Solutions

1. **Point A(3, 4)**:
- After rotation: A' = (-3, -4)

2. **Point B(-2, 5)**:
- After rotation: B' = (2, -5)

3. **Triangle C(1, 1), D(3, 1), E(2, 4)**:
- C' = (-1, -1)
- D' = (-3, -1)
- E' = (-2, -4)
- The vertices of the rotated triangle are C'(-1, -1), D'(-3, -1), E'(-2, -4).

4. **Point F(-7, -3)**:
- After rotation: F' = (7, 3)

5. **Point G(0, -5)**:
- After rotation: G' = (0, 5)

### Additional Practice

If you'd like more practice, here are a few additional questions for you to try on your own:

1. Rotate the point H(4, -2) 180 degrees about the origin.
2. Rotate the point I(-6, -1) 180 degrees about the origin.
3. Rotate the rectangle with vertices J(0, 0), K(2, 0), L(2, 3), and M(0, 3) 180 degrees about the origin.
4. Rotate the point N(-1, 7) 180 degrees about the origin.
5. Rotate the point O(5, 5) 180 degrees about the origin.

### Answers to Additional Practice

1. H' = (-4, 2)
2. I' = (6, 1)
3. J'(0, 0), K'(-2, 0), L'(-2, -3), M'(0, -3)
4. N' = (1, -7)
5. O' = (-5, -5)

Feel free to reach out if you have any questions or need further clarification!