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.

Answer 2

A rotation of figure P must keep a fixed relative angle between its two landmark features, the sharpest corner of the black outer shape and the longest side of the red inner pentagon, since rotating never changes how far apart two features are around the shape, only where that whole pair points. A reflection, on the other hand, flips this relative angle to its mirror value, and a genuinely different figure will not match it at all.

1. A: The sharp corner and the pentagon's long side keep the same relative angle to each other as in P, just turned as a pair to a new overall direction. This matches a rotation.
2. B: The pentagon inside this figure is mirrored relative to the black outline, so the relative angle between the two landmarks has been flipped rather than simply turned. This is a reflection, not a rotation.
3. C: The relative angle between the sharp corner and the pentagon's long side here does not match the value fixed by P at all, so no amount of turning P produces this figure.
4. D: The sharp corner and the long side again keep the same relative angle as in P, only rotated to a different overall direction. This matches a rotation.

Since A keeps the exact relative-angle signature of P, it is a genuine rotation of P (and D passes the same test).

So the correct answer is A.