Question

the image of parallelogram pqrs after a reflection across wy is parallelogram pqrs. rr = 12. what is the length of rz? 3 6 12 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. Here, line $\overleftrightarrow{WY}$ is the line of reflection and $R$ is reflected to $R'$. So, $RZ = ZR'$ and $RR'=RZ + ZR'$.

Step2: Calculate length of $RZ$

Since $RR' = 12$ and $RR'=RZ + ZR'$ and $RZ = ZR'$, we can write the equation $RR'=2RZ$. Then $RZ=\frac{RR'}{2}$. Substituting $RR' = 12$ into the equation, we get $RZ=\frac{12}{2}=6$.

Answer:

6