Question

Consider rotating a figure 90° counter clockwise, 180° counter

clockwise, and 270° counter clockwise. If I were to rotate the same figure
clockwise, list the rotations that result in the same transformed figure.

Answer 1

When you rotate a figure, there are specific angles of rotation that result in the same transformed figure. Here's how it works:

A 90° counter-clockwise rotation is equivalent to a 270° clockwise rotation.

A 180° counter-clockwise rotation is equivalent to a 180° clockwise rotation.

A 270° counter-clockwise rotation is equivalent to a 90° clockwise rotation.

So, if you were to rotate the same figure clockwise, the equivalent rotations would be:

A 90° clockwise rotation is equivalent to a 270° counter-clockwise rotation.

A 180° clockwise rotation is equivalent to a 180° counter-clockwise rotation.

A 270° clockwise rotation is equivalent to a 90° counter-clockwise rotation.

These pairs of rotations will result in the same transformed figure.

Answer 2

When a figure is rotated clockwise, the rotations that result in the same transformed figure are:

1. Rotating the figure 90° clockwise is equivalent to rotating the figure 270° counter clockwise.

2. Rotating the figure 180° clockwise is equivalent to rotating the figure 180° counter clockwise.

3. Rotating the figure 270° clockwise is equivalent to rotating the figure 90° counter clockwise.

These rotations result in the same transformed figure because they have the same angular magnitude, but in opposite directions. Therefore, they produce identical transformations of the original figure.