What you’ll learn
Perform and describe rotations.
Key idea
A quarter-turn counterclockwise maps (x,y) to (-y,x); a half-turn reverses both signs.
Turn direction determines the sign position; a half-turn negates both coordinates and preserves radius.
Worked example
Enter the exact value or ordered values in the format requested below.
Rotate P=(-2,-2) by 180 degrees about the origin. Find its image.
- About the origin, apply (-x,-y) to (-2,-2).
- Image (2,2) preserves squared radius 8; reversing the turn gives preimage (-2,-2).
Answer: (2,2)
Quick Check
Evaluate a worked attempt at perform and describe rotations, identify the first invalid step, and provide the correction.
Rotate P=(1,-1) by 90 degrees counterclockwise about the origin. Student: Step 1, swap coordinate positions to (-1,1). Step 2, negate the second position to (-1,-1). Identify first invalid step and repair.