Question

consider the reflection of parallelogram pqrs across the line of reflection, $overleftrightarrow{wy}$. if rr = 14, then rz = $square$. if sx = 5, then $square$ = 5.

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, for point \( R \) and its image \( R' \), the line \( \overleftrightarrow{WY} \) bisects \( RR' \). Thus, \( RZ = ZR' \) and \( RR' = RZ + ZR' = 2RZ \).

Step2: Calculate \( RZ \)

Given \( RR' = 14 \), from \( RR' = 2RZ \), we solve for \( RZ \): \( RZ=\frac{RR'}{2}=\frac{14}{2} = 7 \).

Step3: Analyze the second part

For point \( S \) and its image \( S' \), the line \( \overleftrightarrow{WY} \) bisects \( SS' \). So, \( SX = XS' \) (since \( X \) is the midpoint of \( SS' \)). Given \( SX = 5 \), then \( XS' = 5 \).

Answer:

For the first blank: \( 7 \)
For the second blank: \( XS' \)