What are the coordinate points of A' if A (5,6) undergoes a rotation of
90° clockwise
180° clockwise
270° clockwise
To find the coordinate points of A' after undergoing a rotation, we can use the rotation matrix formula:
For a 90° clockwise rotation:
[x'] = [0 -1][x]
[y'] = [1 0] [y]
Plugging in the values of A (5,6):
[x'] = [0 -1][5]
[y'] = [1 0] [6]
Simplifying the matrices:
[x'] = [0 -5]
[y'] = [1 0]
Calculating the result:
[x'] = 0 * 5 + (-1) * 6 = -6
[y'] = 1 * 5 + 0 * 6 = 5
Therefore, the coordinate points of A' after a 90° clockwise rotation are (-6, 5).
For a 180° clockwise rotation:
[x'] = [cos(180°) -sin(180°)][x]
[y'] = [sin(180°) cos(180°)][y]
Plugging in the values of A (5,6):
[x'] = [-1 0][5]
[y'] = [0 -1][6]
Simplifying the matrices:
[x'] = [-5 0]
[y'] = [0 -6]
Calculating the result:
[x'] = -1 * 5 + 0 * 6 = -5
[y'] = 0 * 5 + (-1) * 6 = -6
Therefore, the coordinate points of A' after a 180° clockwise rotation are (-5, -6).
For a 270° clockwise rotation:
[x'] = [0 1][x]
[y'] = [-1 0][y]
Plugging in the values of A (5,6):
[x'] = [0 1][5]
[y'] = [-1 0][6]
Simplifying the matrices:
[x'] = [0 5]
[y'] = [-1 0]
Calculating the result:
[x'] = 0 * 5 + 1 * 6 = 6
[y'] = (-1) * 5 + 0 * 6 = -5
Therefore, the coordinate points of A' after a 270° clockwise rotation are (6, -5).