Geometry

Question Analysis:
This question asks you to identify a rotation based on coordinate transformation of a triangle, requiring careful observation of point movements.

Key Concept Explanation:
The rule for a 270° counterclockwise rotation (or 90° clockwise) is:
(x, y) → (y, −x)
90° CCW rotation rule: (x, y) → (-y, x)
A 180° rotation about the origin follows the rule:
(x, y) → (−x, −y)

Step-by-Step Solution:
Apply the rule (x, y) → (y, −x) to each point:
(2, 4) → (4, −2) ✅
(5, 4) → (4, −5) ✅
(5, 2) → (2, −5) ✅
All mapped coordinates match the red triangle.

Option Analysis:
A. 90° clockwise → same as 270° CCW → ✅
B. 180° → (x, y) → (−x, −y) → gives (−2, −4), incorrect
C. ✅ 270° CCW → correct
D. 90° CCW → (x, y) → (−y, ...