Geometry
Rotation
A rotation turns a figure around a center point. Common rotations about the origin: 90° clockwise: (x,y)→(y,−x). 90° counterclockwise: (x,y)→(−y,x). 180°: (x,y)→(−x,−y).
Visualize It
Rotation turns a figure around the origin
Watch & Learn
Watch a clear, friendly video explanation of Rotation:
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Rotate (3, 5) 90° clockwise about the origin
90° clockwise
Step-by-Step Solution
90° clockwise rule: (x, y) → (y, −x)
(3, 5) → (5, −3)
Answer
(5, −3)
Problem
Rotate (−2, 4) 180° about the origin
180° rotation
Step-by-Step Solution
180° rule: (x, y) → (−x, −y)
(−2, 4) → (2, −4)
Answer
(2, −4)
Problem
Rotate (1, 6) 90° counterclockwise about the origin
90° counterclockwise
Step-by-Step Solution
90° counterclockwise rule: (x, y) → (−y, x)
(1, 6) → (−6, 1)
Answer
(−6, 1)
Problem
Rotate (4, −3) 270° counterclockwise (same as 90° clockwise)
270° counterclockwise = 90° clockwise
Step-by-Step Solution
270° counterclockwise = 90° clockwise: (x, y) → (y, −x)
(4, −3) → (−3, −4)
Answer
(−3, −4)
Problem
A point is rotated 360° about the origin. Where does it end up?
360° — back to start
Step-by-Step Solution
A full rotation (360°) brings the point back to its original position.
The point does not move.
Answer
Same position — rotation of 360° is the identity
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Rotate (4, 2) 90° clockwise
Rotate (3, −1) 180°
Rotate (5, 0) 90° counterclockwise
Rotate (−3, 4) 90° clockwise
Rotate (2, 7) 180°
Rotate (6, 1) 90° counterclockwise
Rotate (−4, −2) 180°
Rotate (0, 5) 90° clockwise
Rotate (3, 3) 90° counterclockwise
Rotate (−2, 6) 90° clockwise
Rotate (1, 0) 270° counterclockwise
Rotate (4, −3) 180°
Finished all 12? Give yourself a pat on the back — then check your work!
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