Question

quadrilateral mnpq is rotated 90° counter - clockwise about the origin and then rotated 270° counter - clockwise about the origin. choose all of the statements about the quadrilateral and/or the transformed quadrilateral that are correct. a. the quadrilaterals will be congruent. b. the quadrilateral will map onto itself. c. the quadrilateral will now appear in quadrant iv. d. the quadrilaterals will have the same orientation. e. the quadrilaterals will be similar but not congruent.

Explanation:

Step1: Analyze total rotation

The total counter - clockwise rotation is $90^{\circ}+270^{\circ}=360^{\circ}$.

Step2: Understand rotation properties

A $360^{\circ}$ rotation about the origin is a full - turn. Rigid motions (like rotations) preserve side - lengths and angles, so the pre - image and image are congruent. Also, a $360^{\circ}$ rotation maps a figure onto itself.

Step3: Evaluate option C

The quadrilateral will not move to Quadrant IV as a $360^{\circ}$ rotation leaves it in the same position.

Step4: Evaluate option D

The orientation is the same since it maps onto itself.

Step5: Evaluate option E

The quadrilaterals are congruent (not just similar) because of the rigid - motion rotation.

Answer:

A. The quadrilaterals will be congruent, B. The quadrilateral will map onto itself