Question

parallelogram ( wxyz ) (not shown) is the reflection of parallelogram ( wxyz ) across the ( y - axis ). which statement is true?
a ( overline{wx} ) is parallel to ( overline{wz} )
b ( overline{wx} ) is parallel to ( overline{zy} )
c ( overline{wx} ) is perpendicular to ( overline{wz} )
d ( overline{wx} ) is perpendicular to ( overline{zy} )

Explanation:

Step1: Recall the property of reflection

Reflection across the \(y -\)axis is a transformation. The shape and size of the parallelogram remain the same, and the parallel - perpendicular relationships of the sides remain unchanged. In a parallelogram \(WXYZ\), \(WX\parallel ZY\). After reflection across the \(y -\)axis, for the parallelogram \(W'X'Y'Z'\), the side \(W'X'\) and \(Z'Y'\) still maintain the parallel relationship.

Step2: Analyze each option

• Option A: In a parallelogram, adjacent sides are not parallel. \(W'X'\) and \(W'Z'\) are adjacent sides of the parallelogram \(W'X'Y'Z'\), so \(W'X'\) is not parallel to \(W'Z'\).
• Option B: Since reflection preserves parallelism and in the original parallelogram \(WX\parallel ZY\), then \(W'X'\parallel Z'Y'\).
• Option C: In a parallelogram, adjacent sides are not perpendicular. \(W'X'\) and \(W'Z'\) are adjacent sides of the parallelogram \(W'X'Y'Z'\), so \(W'X'\) is not perpendicular to \(W'Z'\).
• Option D: In a parallelogram, opposite sides are parallel, not perpendicular. \(W'X'\) and \(Z'Y'\) are opposite sides (parallel), not perpendicular.

Answer:

B. \(W'X'\) is parallel to \(Z'Y'\)