Geometry

Question Analysis:
This problem involves deducing a complex transformation from changes in coordinates.
The main focus is on understanding how compound transformations affect position.

Key Concept Explanation:
180° rotation about origin: (x, y) → (−x, −y)
Reflection over y = x: (x, y) → (y, x)
Apply in order to original points.

Step-by-Step Solution:
Start with point A(1, 3):
Step 1: 180° rotation → (−1, −3)
Step 2: Reflect over y = x → (−3, −1) ✅ matches A′
Test point B(4, 3): → 180°: (−4, −3) → y = x: (−3, −4) ✅ matches B′
Test point C(4, 6): → 180°: (−4, −6) → y = x: (−6, −4) ✅ matches C′
So the entire transformation is:
✅ 180° rotation, then reflection over y = x

Option Analysis:
A. x-axis reflection + y-axis ...