Geometry

Question Analysis:
You're asked to determine which transformation(s) can move point A from (3, −2) to (−2, −3).
This involves using rotation rules and possibly chaining them.

Key Concept Explanation:
90° CCW: (x, y) → (−y, x)
180°: (x, y) → (−x, −y)
270° CCW = 90° CW: (x, y) → (y, −x)

Step-by-Step Solution:
A. 90° CW → (x, y) → (y, −x)
→ (3, −2) → (−2, −3) ✅
B. 90° CCW then 180°
Step 1: 90° CCW → (x, y) → (−y, x) → (3, −2) → (2, 3)
Step 2: 180° → (2, 3) → (−2, −3) ✅
C. 270° CCW = 90° CW → Already shown ✅
D. 180°, then 90° CW
Step 1: (3, −2) → (−3, 2)
Step 2: (−3, 2) → (2, 3) ✖
E. Reflection changes coordinate structure; result would be (−2, 3)

Common Mistakes:
Not verifying each step of ...