Question

quadrilateral wxyz will be rotated 180° about the origin and then reflected across the y - axis. 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 ii. d. the quadrilaterals will have the same orientation. e. the quadrilaterals will be similar but not congruent.

Explanation:

Step1: Recall transformation properties

A rotation of 180° about the origin and a reflection across the y - axis are rigid transformations.

Step2: Understand rigid - transformation result

Rigid transformations preserve side - lengths and angles. So, the pre - image and the image are congruent.

Step3: Analyze mapping onto itself

The given sequence of transformations does not map the quadrilateral onto itself in general.

Step4: Determine quadrant location

The original quadrilateral in Quadrant III, after 180° rotation about the origin, it goes to Quadrant I, and after reflection across the y - axis, it goes to Quadrant II. But this is not the only correct statement.

Step5: Check orientation

The orientation of the quadrilateral changes with these transformations.

Step6: Evaluate similarity and congruence

Since rigid transformations are involved, the quadrilaterals are congruent (not just similar). So, the only correct statement is that the quadrilaterals will be congruent.

Answer:

A. The quadrilaterals will be congruent.