Question

Which of the options is/are rotations of the figure P?

• A. A
• B. B
• C. C
• D. D

Hint:

To solve rotation problems, pick a distinctive feature or a pair of features on the original object. Then, track how this feature transforms in each option. If the relative positions and orientations are preserved, it's a rotation. If they are mirrored, it's a reflection.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a spatial reasoning problem. We need to determine which of the figures (A, B, C, D) can be obtained by simply rotating Figure P in the 2D plane, without any flipping (reflection).
Step 2: Detailed Explanation:
Let's analyze Figure P. It consists of a black, irregular outer shape and an inner red pentagon. A key feature is the relationship between the two shapes, for example, the orientation of the longest side of the red pentagon relative to the sharpest corner of the black shape.

Figure P: The longest side of the red pentagon is at the bottom-left. The sharpest corner of the black shape is at the top-right.
Option A: This figure appears to be a counter-clockwise rotation of P. The sharpest corner is now at the top-left, and the longest side of the red pentagon is at the top. This orientation is consistent with a rotation of P. Thus, A is a rotation.
Option B: In this figure, the internal pentagon appears to be a mirror image of the one in P. If we rotate P to align the black shape with B, the pentagon inside will not match. This is a reflection, not a rotation. Thus, B is not a rotation.
Option C: The orientation of the pentagon relative to the black outer shape does not match any possible rotation of P. For instance, if we rotate P so its longest red side is at the top (as in C), the sharpest black corner would be at the bottom-left, not the bottom-right as shown. Thus, C is not a rotation.
Option D: This figure is a clockwise rotation of P. The sharpest corner is now at the bottom-right, and the longest side of the red pentagon is at the top-right. This configuration is consistent with a simple rotation of P. Thus, D is a rotation.

Step 3: Final Answer:
Figures A and D are the only options that are pure rotations of figure P.