Question

the image of parallelogram pqrs after a reflection across \overleftrightarrow{wy} is parallelogram pqrs. \\( rr = 12 \\). what is the length of rz? \\( \bigcirc \\ 3 \\) \\( \bigcirc \\ 6 \\) \\( \bigcirc \\ 12 \\) \\( \bigcirc \\ 18 \\)

Explanation:

Step1: Recall Reflection Property

In a reflection, the line of reflection (here, \(\overleftrightarrow{WY}\)) is the perpendicular bisector of the segment joining a point and its image (e.g., \(RR'\)). So, \(Z\) is the midpoint of \(RR'\).

Step2: Calculate \(RZ\)

Since \(Z\) is the midpoint, \(RZ=\frac{1}{2}RR'\). Given \(RR' = 12\), then \(RZ=\frac{12}{2}=6\).

Answer:

6