What are the coordinate points of A' (3,5) if A undergoes a rotation of:

Question

90 degrees clockwise:
180 degrees clockwise:
270 degrees clockwise:

Answer 1

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).