Question

the image of parallelogram pqrs after a reflection across wy is parallelogram pqrs. rr = 12. what is the length of rz? 12 6 3 18

Explanation:

Step1: Recall reflection property

In a reflection, the line of reflection is the perpendicular - bisector of the segment joining a point and its image. So, if \(R\) is reflected across line \(\overleftrightarrow{WY}\) to get \(R'\), then \(RZ = R'Z\) and \(RR'=RZ + R'Z\).

Step2: Calculate \(RZ\)

Since \(RR' = 12\) and \(RR'=RZ + R'Z\) and \(RZ = R'Z\), we can write the equation \(12=2RZ\). Solving for \(RZ\), we divide both sides of the equation by 2: \(RZ=\frac{12}{2}=6\).

Answer:

6