Which option(s) is/are simple rotations of the figure given below?
Show Hint
When checking for rotations, pick a unique feature or a combination of adjacent features in the original image. Then, locate that same feature in each option and verify if the entire surrounding pattern is consistent with the original. If any relative position is changed, it's not a simple rotation.
Step 1: Understanding the Concept:
The problem asks us to identify which of the given options are identical to the original figure, but simply rotated. This means the sequence of colors and their relative positions within each concentric ring must be preserved. We need to check for any changes in the pattern itself, such as mirrored sections or swapped colors, which would make an option different from a simple rotation.
Step 2: Detailed Explanation:
Let's establish a reference point in the original figure. For example, let's look at the outermost ring at the 12 o'clock position, which has a brown segment. We will track this and the adjacent colors as we rotate the figure.
Original Figure: At the top (12 o'clock), the color sequence from outside to inside is Brown → Pink → Green → Blue → Red (center).
Option A: This figure is a simple clockwise rotation of the original. The brown segment from the outer ring is now at the 1 o'clock position. The sequence of colors in all rings is preserved relative to each other. Thus, A is a simple rotation.
Option B: Let's find the brown segment in the outermost ring. It's at the 1 o'clock position, same as in A. However, look at the ring next to it (the pink/teal ring). In the original, the segment next to the outer brown one is pink. In option B, it is teal. The color pattern has been altered. Therefore, B is not a simple rotation.
Option C: Let's again find the outer brown segment. It is at the 7 o'clock position. The segment next to it in the second ring should be pink. In option C, it is teal. The pattern is altered. Therefore, C is not a simple rotation. It appears to be a mirror image (reflection) of the original.
Option D: The outer brown segment is at the 6 o'clock position. If we follow the color pattern from this point, it matches the original figure's pattern perfectly, just rotated by 180 degrees. For example, at the 6 o'clock position, the sequence from outside-in is Brown → Pink → Green → Blue → Red, which is consistent with the original. Thus, D is a simple rotation.
Step 3: Final Answer:
Options A and D are simple rotations of the original figure. Options B and C contain alterations to the color pattern and are not simple rotations.
