Question

△abc is the image of △abc under a rotation about point b. determine the angles of rotation. choose all answers that apply: a 90° clockwise b 90° counterclockwise c 180° d 270° clockwise e 270° counterclockwise

Explanation:

Step1: Analyze rotation direction visually

By observing the position of $\triangle ABC$ and $\triangle A'B'C'$, we can see that the rotation is counter - clockwise.

Step2: Check angle measures

We know that a $90^{\circ}$ counter - clockwise rotation would turn a figure a quarter - turn counter - clockwise and a $270^{\circ}$ counter - clockwise rotation would turn a figure three - quarters of a turn counter - clockwise. Visually, the rotation from $\triangle ABC$ to $\triangle A'B'C'$ is a $90^{\circ}$ counter - clockwise rotation. Also, a $270^{\circ}$ clockwise rotation is equivalent to a $90^{\circ}$ counter - clockwise rotation.

Answer:

B. $90^{\circ}$ counterclockwise
D. $270^{\circ}$ clockwise