Question

point ( a ) is the image of point ( a ) under a rotation about point ( q ).

determine the angles of rotation.

choose all answers that apply:

a ( 90^{circ} ) clockwise

b ( 90^{circ} ) counterclockwise

c ( 180^{circ} )

d ( 270^{circ} ) clockwise

e ( 270^{circ} ) counterclockwise

Explanation:

Step1: Understand rotation properties

A rotation of \(90^{\circ}\) clockwise is equivalent to a rotation of \(270^{\circ}\) counter - clockwise. A rotation of \(90^{\circ}\) counter - clockwise is equivalent to a rotation of \(270^{\circ}\) clockwise.

Step2: Analyze the given points

By visual inspection (assuming a standard coordinate - like mental model for rotation about a point), if we consider the general direction of rotation. A \(270^{\circ}\) clockwise rotation (which is the same as \(90^{\circ}\) counter - clockwise in terms of the final position of a point after rotation about a center) can map point \(A\) to \(A'\). Also, a \(90^{\circ}\) counter - clockwise rotation (which is the same as \(270^{\circ}\) clockwise) can achieve the mapping from \(A\) to \(A'\).

Answer:

B. \(90^{\circ}\) counterclockwise, D. \(270^{\circ}\) clockwise