When faced with complex visual puzzles, especially "odd one out" types, check for fundamental geometric properties like symmetry (rotational, reflectional), number of intersections, or topological equivalence.
Step 1: Understanding the Concept:
This question appears to be a "find the odd one out" puzzle based on the four figures in the bottom row, labeled A, B, C, and D. The figures in the top row seem to be part of a different, potentially malformed question and can be disregarded. We need to find a property that is shared by three of the options but not by the fourth.
Step 2: Detailed Explanation:
Let's analyze the geometric properties of the pairs of paths in options A, B, C, and D. A key property to examine in such figures is symmetry. We will check if there is a symmetrical relationship between the two paths in each option.
Option B: Let's test for 180-degree rotational symmetry (point symmetry) around the center of the figure. If we take any point on the left path and rotate it 180 degrees about the center, it lands on a corresponding point on the right path. For example, the start point of the left path (top-left) corresponds to the end point of the right path (bottom-right). This figure possesses point symmetry.
Option C: Similarly, this figure also exhibits point symmetry between the two paths. The path on the left is a 180-degree rotation of the path on the right about the center.
Option D: This figure also possesses point symmetry. The complex path on the left, when rotated 180 degrees, becomes the path on the right.
Option A: Let's check this figure for point symmetry. The left path starts at the top-left. Its corresponding point under 180-degree rotation would be at the bottom-right. However, the right path does not end there; it ends at the top-right. Therefore, the paths in figure A are not point-symmetric.
Step 3: Final Answer:
Figures B, C, and D all share the property of having central point symmetry between their two paths. Figure A is the only one that lacks this property. Therefore, A is the odd one out.
