Geometry

Question Analysis:
This problem tests your ability to recognize a composite transformation from a coordinate rule.

Key Concept Explanation:
Rotation 180° about the origin: (x, y) → (−x, −y)
Then translation:
 x → x + 2 (right 2)
 y → y + 5 (up 5)
Final: (−x + 2, −y + 5)

Step-by-Step Solution:
Rotate: (x, y) → (−x, −y)
Translate: (−x + 2, −y + 5) ✅

Option Analysis:
A: reflection over origin = 180° rotation, so close — but translation is incorrect ❌
B: x-axis reflection flips y only ❌
C: correct ✅<...