What you’ll learn
Understand rotations.
Key idea
Clockwise and counterclockwise quarter turns swap coordinates with different signs; radius to the center is preserved.
Keep center fixed; opposite directions differ in signed swap and preserve radius.
Worked example
Classify examples and non-examples for the concept 'Understand rotations'.
Rotate (-2,-2) 90 degrees counterclockwise about the origin. Classify proposed image (-2, 2) with rule evidence.
- A 90-degree counterclockwise turn about the fixed origin follows (x,y)→(-y,x).
- Applying it gives (-2,-2)→(2, -2) and (2, 2)→(-2, 2); both have unchanged squared distance to the center.
Answer: False — (x,y)→(-y,x) gives actual image (2, -2).
Quick Check
Classify examples and non-examples for the concept 'Understand rotations'.
Rotate (1,-1) 90 degrees clockwise about the origin. Classify proposed image (-1, -1) with rule evidence.