Geometry

Question Analysis:  
This question tests sequential reflections over intersecting lines in coordinate geometry and their composite effect.  

Key Concept Explanation:  
- Reflection over y = x: Swaps the x- and y-coordinates.  
- Reflection over y = -x: Swaps and negates the x- and y-coordinates.  
- Composite effect: Two reflections over lines intersecting at 90° result in a 180° rotation about the intersection point (the origin).  

Step-by-Step Solution:  
1. First reflection (over y = x):  
  - Original point: (3, 4)  
  - After reflection: (4, 3) (swap coordinates).  
2. Second reflection (over y = -x):  
  - Current point: (4, 3)  
  - After reflection: (-3, -4) (swap and negate coordinates).
3. Verification:  
  - A 180° rotation of (3, 4) about the origin directly gives (-3, -4).

Option Analysis:  
- A) Correct – Matches the final position after both reflections (or a 180° rotation).  
- B) Incorrect – This would occur if the reflections w...