Question

concept rotations
a rotation ( r_{(x^{circ}, 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^{prime}=p )).
• for a preimage point ( a, p a=p a^{prime} ) and ( m angle a p a^{prime}=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. ( r_{270^{circ}} )

is a reflection at ( 270^{circ} )
is a ccw rotation about ( (2,1) )
is a cw rotation, where the center
of rotation is at ( (0,0) )
is a ccw rotation, where the center
of rotation is at the origin.

Explanation:

A rotation \( r_{270^{\circ}} \) is a counter - clockwise (ccw) rotation. The standard notation \( r_{x^{\circ}} \) (where \( x = 270\) here) implies a counter - clockwise rotation about the origin \((0,0)\) (by default, if no other center is specified). A reflection is a different type of transformation (it flips over a line, not rotates). Also, the center of rotation is at the origin unless stated otherwise.

Answer:

Is a ccw rotation, where the center of rotation is at the origin.