The given figure is reflected about the horizontal dashed line and then rotated clockwise by 90° about an axis perpendicular to the plane of the figure.

Which one of the following options correctly shows the resultant figure?

Correct Answer:

Step-by-Step Explanation:

To determine the resultant figure, we follow the two transformations given in the question in sequence: vertical reflection (reflection across the horizontal line) followed by a 90° clockwise rotation.

Original Figure:

Let us identify the position of each component in the 2×2 grid of the original figure:
• Top-Left (TL): Lightning bolt icon pointing towards the center.
• Top-Right (TR): Corner shape (L-like polygon) pointing vertically downward and right.
• Bottom-Left (BL): Two-headed L-arrow pointing Up and Left.
• Bottom-Right (BR): Crescent moon opening towards the left (C-shape).

Step 1: Reflection about the horizontal dashed line (Vertical Flip)

When reflecting an image vertically across a horizontal axis:
• Top components move to the Bottom, and Bottom components move to the Top.
• Left and Right positions remain unchanged.
• Individual shapes flip vertically (upside-down).

Position changes after Step 1:
• Top-Left: Two-headed L-arrow (flipped vertically: arrow that pointed Up now points Down, while arrow pointing Left remains pointing Left).
• Top-Right: Crescent moon (flipped vertically: arc curves downward instead of upward).
• Bottom-Left: Lightning bolt (flipped vertically).
• Bottom-Right: Corner L-shape (flipped vertically).

Step 2: Clockwise rotation by 90°

When rotating the entire grid 90° clockwise:
• The element at Top-Left (TL) moves to Top-Right (TR).
• The element at Top-Right (TR) moves to Bottom-Right (BR).
• The element at Bottom-Right (BR) moves to Bottom-Left (BL).
• The element at Bottom-Left (BL) moves to Top-Left (TL).

Let's track where each feature ends up in the final grid:
1. Lightning bolt: Moves from Bottom-Left to Top-Left (TL) and rotates 90° clockwise.
2. Two-headed L-arrow: Moves from Top-Left to Top-Right (TR) and rotates 90° clockwise (the arrow pointing Down becomes pointing Left, and the arrow pointing Left becomes pointing Up).
3. Corner L-shape: Moves from Bottom-Right to Bottom-Left (BL) and rotates 90° clockwise.
4. Crescent moon: Moves from Top-Right to Bottom-Right (BR) and rotates 90° clockwise (appearing as an inverted U-shaped arch).

Comparing these positions with the options, the resulting arrangement matches the figure shown below: