The coordinates of R when rotated about the origin by 90 degrees clockwise, 180 degrees, and 270 degrees clockwise are (-3, 4), (-4, -3), and (3, -4), respectively.
When rotating a point about the origin, we can use the following rotation matrices:
90 degrees clockwise: [[0, -1], [1, 0]]
180 degrees: [[-1, 0], [0, -1]]
270 degrees clockwise: [[0, 1], [-1, 0]]
To rotate point R about the origin, we simply multiply its coordinates by the corresponding rotation matrix.
a) 90 degrees clockwise
R = (4, 3)
R_rotated = [[0, -1], [1, 0]] * R
R_rotated = (-3, 4)
b) 180 degrees
R = (4, 3)
R_rotated = [[-1, 0], [0, -1]] * R
R_rotated = (-4, -3)
c) 270 degrees clockwise
R = (4, 3)
R_rotated = [[0, 1], [-1, 0]] * R
R_rotated = (3, -4)
Therefore, the coordinates of R when rotated about the origin by 90 degrees clockwise, 180 degrees, and 270 degrees clockwise are (-3, 4), (-4, -3), and (3, -4), respectively.
Image confirmation
The image you provided confirms the above calculations. When point R is rotated 90 degrees clockwise, it moves to the point (-3, 4).
When it is rotated 180 degrees, it moves to the point (-4, -3). And when it is rotated 270 degrees clockwise, it moves to the point (3, -4).