Answer:
To rotate a point 90 degrees clockwise about another point, you can follow these steps:
1. Subtract the coordinates of the center of rotation from the coordinates of the point you want to rotate to translate the center of rotation to the origin.
A translated point A would be: (5 - 0, 4 - 1) = (5, 3)
2. Perform the rotation by swapping the x and y coordinates and negating the new x-coordinate.
The rotated point A' would be: (3, -5)
3. Add the coordinates of the original center of rotation to the rotated coordinates to translate the origin back to the center of rotation.
The final coordinates of point A' would be: (3 + 0, -5 + 1) = (3, -4)
Therefore, the coordinates of point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).