Question

Which of the options is/are simple rotations of the figure given below? 

 

• A. A
• B. B
• C. C
• D. D

Hint:

To check for rotation, focus on an asymmetric part of the pattern. Track its position and orientation as you mentally rotate the figure. If you can match it in another option, it's a rotation. If you can only match it by flipping it over (like looking in a mirror), it's a reflection.

Answer 1

The Correct Option is A, B, C

Step 1: Understanding the Concept:
This question tests the ability to recognize a 2D pattern regardless of its orientation. A "simple rotation" means the figure is turned around its center without being flipped or otherwise distorted. We need to identify which of the options (A, B, C, D) show the same intrinsic pattern as the original tilted figure. Step 2: Detailed Explanation:
First, let's analyze the core pattern of the given figure, ignoring its initial 45-degree tilt. We can describe the pattern by the relative positions of the colored blocks. - There is a central 2x2 block of light purple squares. - Adjacent to the left side of this purple block is a 2x1 vertical cyan block. - Adjacent to the top side of the purple block is a 1x2 horizontal cyan block. - Black squares fill the remaining space. Now, let's examine each option to see if it contains this same pattern, possibly rotated. (A) This figure is shown in an upright orientation. It has the central 2x2 purple block. It has the 2x1 vertical cyan block to its left and the 1x2 horizontal cyan block above it. This perfectly matches our description of the core pattern. Therefore, A is a simple rotation of the original figure (specifically, a 45-degree counter-clockwise rotation). A is correct. (B) This figure has the central 2x2 purple block. A 2x1 vertical cyan block is to its right, and a 1x2 horizontal cyan block is below it. If we rotate figure A by 180 degrees, the left cyan block will move to the right, and the top cyan block will move to the bottom. This matches figure B exactly. Therefore, B is a 180-degree rotation of A and thus a simple rotation of the original figure. B is correct. (C) This figure has the central 2x2 purple block. A 2x1 vertical cyan block is to its left, and a 1x2 horizontal cyan block is below it. If we rotate figure A by 270 degrees clockwise (or 90 degrees counter-clockwise), the left vertical cyan block moves to the bottom and becomes a horizontal block. The top horizontal cyan block moves to the left and becomes a vertical block. This matches figure C exactly. Therefore, C is a 270-degree rotation of A and a simple rotation of the original figure. C is correct. (D) This figure has the central 2x2 purple block. A 2x1 vertical cyan block is to its right, and a 1x2 horizontal cyan block is above it. This pattern cannot be achieved by rotating figure A. It is a horizontal reflection (flip) of figure A. A reflection is not a simple rotation. D is incorrect. Step 3: Final Answer:
Figures A, B, and C all represent the same underlying pattern at different rotational orientations (0, 180, and 270 degrees, respectively, relative to A's orientation). Figure D is a reflection. Thus, A, B, and C are the correct options.