Question

quadrilateral wxyz will be reflected across the x - axis and then rotated 90° counterclockwise about the origin. choose all of the statements that are correct. a. the quadrilaterals will be congruent. b. the quadrilateral will map onto itself. c. the quadrilaterals will be in the same quadrant. d. the quadrilaterals will be similar but not congruent.

Explanation:

Step1: Recall transformation properties

Reflections and rotations are rigid - motions. Rigid - motions preserve side lengths and angle measures.

Step2: Analyze congruence

Since reflections and rotations are rigid - motions, the pre - image and the image of the quadrilateral WXYZ after reflection across the x - axis and 90° counter - clockwise rotation about the origin will be congruent. So, statement A is correct.

Step3: Analyze self - mapping

A 90° counter - clockwise rotation and a reflection across the x - axis do not map a non - symmetric quadrilateral onto itself. So, statement B is incorrect.

Step4: Analyze quadrant location

The original quadrilateral is in the first and second quadrants. After reflection across the x - axis, it will be in the third and fourth quadrants, and after a 90° counter - clockwise rotation about the origin, it will be in the second and third quadrants. So, it will not be in the same quadrant as the original. Statement C is incorrect.

Step5: Analyze similarity and congruence

Since the transformations are rigid - motions, the quadrilaterals are congruent (and congruent figures are also similar). But the statement says they are similar but not congruent, so statement D is incorrect.

Answer:

A. The quadrilaterals will be congruent.