What are the coordinate points of A' (5,2) if A undergoes a rotation of: 90°clockwise 180°clockwise 270°clockwise

Answer 1

To find the new coordinate points of A' after it undergoes a rotation, we can use the rotation matrix.

1. 90° clockwise rotation:
The rotation matrix for a 90° clockwise rotation is:
[0, -1]
[1, 0]

Using this matrix, we can multiply it with the original coordinate point of A (5, 2):
[0, -1] * [5]
[1, 0] * [2]

Multiplying the matrices gives us:
[0*(-1) + -1*2]
[1*5 + 0*2]
[-2]
[5]

Therefore, the new coordinate point A' after a 90° clockwise rotation is (-2, 5).

2. 180° clockwise rotation:
The rotation matrix for a 180° clockwise rotation is:
[-1, 0]
[0, -1]

Using this matrix, we can multiply it with the original coordinate point of A (5, 2):
[-1*5 + 0*2]
[0*(-1) + -1*2]
[-5]
[-2]

Therefore, the new coordinate point A' after a 180° clockwise rotation is (-5, -2).

3. 270° clockwise rotation:
The rotation matrix for a 270° clockwise rotation is:
[0, 1]
[-1, 0]

Using this matrix, we can multiply it with the original coordinate point of A (5, 2):
[0*1 + 1*2]
[-1*5 + 0*2]
[2]
[-5]

Therefore, the new coordinate point A' after a 270° clockwise rotation is (2, -5).