Rotating a figure 90 degrees clockwise about a point is a fundamental transformation in geometry. To perform this rotation, follow these steps:
- Identify the point of rotation: This is the point around which the figure will be rotated. It can be a vertex of the figure or any other point on the coordinate plane.
- Determine the original coordinates: Write down the coordinates of the point(s) in the figure you want to rotate. Let’s say the point of rotation is (h, k) and a point in the figure is (x, y).
- Translate the figure: Move the entire figure so that the point of rotation (h, k) is at the origin. You do this by subtracting h from x and k from y, which gives you (x – h, y – k).
- Apply the rotation: To rotate the point (x – h, y – k) 90 degrees clockwise, switch the coordinates and change the sign of the new y-coordinate. This transforms it into (y – k, -(x – h)).
- Translate back: After rotation, move the point back to its original location by adding h and k. So now you have (y – k + h, -(x – h) + k).
Repeat this process for all points in the figure to complete the rotation. After you have done this for every point, you will have your figure rotated 90 degrees clockwise around the specified point.
For example, if you are rotating the point (2, 3) about the point (1, 1):
- Translate: (2 – 1, 3 – 1) = (1, 2)
- Rotate: (2, -1)
- Translate back: (2 + 1, -1 + 1) = (3, 0)
The new position of the point (2, 3) after a 90-degree clockwise rotation about (1, 1) is (3, 0).