Question

an angle inscribed in the coordinate - plane has a measure of 120°. which of the following statements are true? select two that apply. a. after a translation 9 units, the angle will no longer measure 120°. b. after a 270 - clockwise rotation about the origin, the angle will no longer measure 120°. c. after a dilation through the origin by a scale factor of 1/4, the angle will no longer measure 120°. d. after a reflection over the x - axis, the angle will still measure 120°. e. after a 90 - counterclockwise rotation about the origin, the angle will still measure 120°.

Explanation:

Step1: Recall transformation properties

Translation, reflection, and rotation are rigid - motions. Rigid - motions preserve angle measures. Dilation is not a rigid - motion but it does not change the angle measure.

Step2: Analyze each option

• Option A: Translation is a rigid - motion. It does not change the angle measure. So, this statement is false.
• Option B: A $270^{\circ}$ clock - wise rotation is a rigid - motion. It changes the orientation but not the angle measure. So, this statement is false.
• Option C: Dilation does not change the angle measure. So, this statement is false.
• Option D: Reflection is a rigid - motion. It preserves the angle measure. So, the angle will still measure $120^{\circ}$. This statement is true.
• Option E: A $90^{\circ}$ counter - clockwise rotation is a rigid - motion. It changes the orientation but not the angle measure. So, the angle will still measure $120^{\circ}$. This statement is true.

Answer:

D. After a reflection over the x - axis, the angle will still measure $120^{\circ}$; E. After a $90^{\circ}$ counterclockwise rotation about the origin, the angle will still measure $120^{\circ}$