Question

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

Explanation:

Step1: Recall the property of reflection

When a figure is reflected across a line, the line of reflection is the perpendicular bisector of the segment joining a point and its image. So, \(RZ = R'Z\) and \(RR'=RZ + R'Z\).

Step2: Substitute and solve

Since \(RR' = 12\) and \(RR'=RZ + R'Z\) and \(RZ = R'Z\), we have \(12=RZ + RZ\). Let \(RZ=x\), then \(12 = 2x\). Solving for \(x\), we get \(x=\frac{12}{2}=6\).

Answer:

6