Geometry

Question Analysis:
This question evaluates the ability to combine two rotations of different directions and magnitudes into a single net rotation.

Key Concept Explanation:
Rotations can be added by converting them to the same direction (CCW is standard).
90° clockwise (CW) = 270° counterclockwise (CCW).
Total rotation = Sum of individual rotations (simplify modulo 360°).

Step-by-Step Solution:
Convert all rotations to CCW:
First rotation: 270° CCW (given).
Second rotation: 90° CW = 270° CCW.
Add rotations: 270° CCW + 270° CCW = 540° CCW
Simplify modulo 360°: 540° − 360° = 180° CCW

Option Analysis:
A) Incorrect: Would require rotations to cancel exactly.
B) Incorrect: Underestimates the net rotation.
C) Correct: Net rotation is 180° CCW.
D) Incorrect: Overestimates the net rotation.

Common Mistakes:
Not converting directions: Adding 270° CCW + 90° CW directly without converti...