Question

the image of trapezoid pqrs after a reflection across (overleftrightarrow{wy}) is trapezoid pqrs. what is the relationship between (overline{rr}) and (overline{ss})? rr = 2ss rr = 4ss (overline{rr}paralleloverline{ss}) (overline{rr}perpoverline{ss})

Explanation:

Step1: Recall reflection property

In a reflection, the line segment connecting a point and its image is perpendicular to the line of reflection. Let the line of reflection be $\overleftrightarrow{WY}$. Points $R$ and $R'$ are related by reflection, and points $S$ and $S'$ are related by reflection. The line - segments $\overline{RR'}$ and $\overline{SS'}$ are both perpendicular to the line of reflection $\overleftrightarrow{WY}$.

Step2: Determine the relationship

If two lines are perpendicular to the same line, then they are parallel to each other. So, $\overline{RR'}\parallel\overline{SS'}$. There is no information given to suggest a ratio relationship like $\overline{RR'}=2\overline{SS'}$ or $\overline{RR'}=4\overline{SS'}$, and they are not perpendicular to each other.

Answer:

C. $\overline{RR'}\parallel\overline{SS'}$