Geometry

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

Key Concept Explanation:
The solution requires understanding of:
y = -x reflection: (x, y) → (-y, -x)
Translation: (x, y) → (x + h, y + k) where h = 2, k = 4
y-axis reflection: (x, y) → (-x, y)

Step-by-Step Solution:
First transformation (y = -x reflection): (3, -1) → (1, -3)
Second transformation (translation right 2, up 4): (1, -3) → (3, 1)
Final transformation (y-axis reflection): (3, 1) → (-3, 1)

Common Mistakes:
Forgetting to swap coordinates in y = -x reflection
Subtracting instead of adding for right/up translation
Negl...