Question

concept rotations
a rotation ( r_{(x, p)} ) is a transformation that rotates each point in the preimage about a point ( p ), called the center of rotation, by an angle measure of ( x^{circ} ), called the angle of rotation. a rotation has these properties:

• the image of ( p ) is ( p ) (that is, ( p = p )).
• for a preimage point ( a, p a = p a ) and ( m angle a p a = x^{circ} ).

a rotation is a rigid motion, so length and angle measure are preserved. note that a rotation is counterclockwise for a positive angle measure.

1. all rotations are a rigid motion
2. a rotation is ccw if it is a negative angle

Explanation:

• For question 15: A rotation is a rigid motion. Rigid motions preserve length and angle measure. Since a rotation has the property that \(PA = PA'\) (lengths are equal) and angle measures are preserved ( \(m\angle APA'=x^{\circ}\) ), all rotations are rigid motions.
• For question 16: A rotation is counter - clockwise (ccw) for a positive angle measure. A negative - angle rotation is clockwise (cw).

Answer:

1. True
2. False