What are the coordinate points of A' (3,5) if A undergoes a rotation of:
90 degrees clockwise:
180 degrees clockwise:
270 degrees clockwise:
To find the coordinate points of A' after a rotation, we need to apply the appropriate rotation matrix.
1. 90 degrees clockwise rotation:
The rotation matrix for a 90 degrees clockwise rotation is:
| 0 1 |
| -1 0 |
To apply the rotation matrix to point A(3,5), we multiply the matrix by the coordinate vector:
| 0 1 | | 3 | | -5 |
| -1 0 | * | 5 | = | 3 |
So, A' after a 90 degrees clockwise rotation is (-5,3).
2. 180 degrees clockwise rotation:
The rotation matrix for a 180 degrees clockwise rotation is:
| -1 0 |
| 0 -1 |
Applying the matrix to A(3,5):
| -1 0 | | 3 | | -3 |
| 0 -1 | * | 5 | = | -5 |
A' after a 180 degrees clockwise rotation is (-3,-5).
3. 270 degrees clockwise rotation:
The rotation matrix for a 270 degrees clockwise rotation is:
| 0 -1 |
| 1 0 |
Applying the matrix to A(3,5):
| 0 -1 | | 3 | | -5 |
| 1 0 | * | 5 | = | 3 |
A' after a 270 degrees clockwise rotation is (-5,3).