Geometry

Question Analysis:
This problem examines three consecutive coordinate transformations, with the key operation being reflection across y = -x followed by translation and x-axis reflection.

Key Concept Explanation:
The solution requires:
y = -x reflection: (x, y) → (-y, -x)
Translation: (x, y) → (x - 4, y - 3)
x-axis reflection: (x, y) → (x, -y)

Step-by-Step Solution:
First transformation (y = -x reflection): (-2, 5) → (-5, 2)
Second transformation (translation left 4, down 3): (-5, 2) → (-9, -1)
Final transformation (x-axis reflection): (-9, -1) → (-9, 1)

Common Mistakes:
Forgetting to swap coordinates in y = -x reflection
Adding instead of subtracting for left/down translation
Neglecting to change y-sign in x-axis reflection
Pe...