What are the coordinate points of A' if A (5,6) undergoes a rotation of 90° clockwise 270° clockwise

Answer 1

To find the coordinate points of A' after a rotation, you need to first determine the direction and angle of rotation.

For the first rotation of 90° clockwise, the coordinates of A' can be found by using the rotation matrix for a 90° clockwise rotation:

| cos(theta) sin(theta) | | 5 | | -1 |
| -sin(theta) cos(theta) | x | 6 | = | 5 |

Substituting the value of theta as -90°:

| cos(-90°) sin(-90°) | | 5 | | -1 |
| -sin(-90°) cos(-90°) | x | 6 | = | 5 |

Simplifying the matrix multiplication:

| 0 -1 | | 5 | | -1 |
| 1 0 | x | 6 | = | 5 |

Multiplying the matrices:

| -1 |
| 6 |

So, the coordinates of A' after a rotation of 90° clockwise are (-1, 6).

Now, for the second rotation of 270° clockwise, we need to rotate point A' (-1, 6):

| cos(theta) sin(theta) | | -1 | | -6 |
| -sin(theta) cos(theta) | x | 6 | = | 1 |

Substituting the value of theta as -270°:

| cos(-270°) sin(-270°) | | -1 | | -6 |
| -sin(-270°) cos(-270°) | x | 6 | = | 1 |

Simplifying the matrix multiplication:

| 0 1 | | -1 | | -6 |
| -1 0 | x | 6 | = | 1 |

Multiplying the matrices:

| 6 |
| -1 |

So, the coordinates of A' after a rotation of 270° clockwise are (6, -1).