Geometry

Question Analysis:
This problem examines three consecutive transformations of a point, with primary focus on the y = -x reflection 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 = 3, k = 2
y-axis reflection: (x, y) → (-x, y)

Step-by-Step Solution:
First transformation (y=-x reflection): (1, -4) → (4, -1)
Second transformation (translation right 3, up 2): (4, -1) → (7, 1)
Final transformation (y-axis reflection): (7, 1) → (-7, 1)

Common Mistakes:
Forgetting to negate x-coordinate in final reflection
Miscalculating the initial y = -x reflection
Confusing translation directions (right/up vs left/do...