Definition: A rotation is a transformation that turns every point of a figure by a given angle around a fixed point called the center of rotation.
What is a rotation?
It is a turn. A rotation needs three things: a center, an angle, and a direction, clockwise or counterclockwise.
What are the origin rules?
Counterclockwise about the origin:
- 90 degrees: (x, y) becomes (-y, x).
- 180 degrees: (x, y) becomes (-x, -y).
- 270 degrees: (x, y) becomes (y, -x).
What does an example look like?
Rotate Q(4, 1) by 90 degrees counterclockwise about the origin. The rule gives (-1, 4). Rotate it 180 degrees: (-4, -1).
For a triangle A(1, 0), B(3, 0), C(3, 2), a 90 degree turn gives A'(0, 1), B'(0, 3), C'(-2, 3).
What is preserved?
Distances and angle measures, so the image is congruent. Each point stays the same distance from the center.
How do clockwise turns convert?
A 90 degree clockwise turn equals a 270 degree counterclockwise turn.
What is a common mistake?
Using the wrong direction. Positive angles are counterclockwise unless the problem says otherwise.