Question

applying the formal definition of reflection
consider the reflection of parallelogram pqrs across the line of reflection, (overleftrightarrow{wy}).
if (rr = 14), then (rz=).
if (sx = 5), then (=5).

Explanation:

Step1: Recall the property of reflection

In a reflection, the line of reflection is the perpendicular bisector of the segment joining a point and its image. So, if \(RR' = 14\), then \(RZ=\frac{1}{2}RR'\).

$$RZ=\frac{1}{2}\times14$$

Step2: Calculate \(RZ\)

$$RZ = 7$$

Step3: Recall the property of reflection for the second part

Since \(S\) and \(S'\) are reflections across the line \(WY\), and \(SX\) and \(XS'\) are related by the reflection property. If \(SX = 5\), then \(XS'=5\) (because the distance from a point to the line of reflection is equal to the distance from its image to the line of reflection)

Answer:

\(RZ = 7\); \(XS'=5\)