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 joining a point and its image is perpendicular to the line of reflection. And for any two points and their respective images, the line - segments joining them are parallel. Here, points \(R\) and \(R'\) are related by reflection across \(\overleftrightarrow{WY}\), and points \(S\) and \(S'\) are related by reflection across \(\overleftrightarrow{WY}\).
The line - segments \(\overline{RR'}\) and \(\overline{SS'}\) are both perpendicular to the line of reflection \(\overleftrightarrow{WY}\).

Step2: Determine the relationship

Since two lines that are perpendicular to the same line are parallel to each other, \(\overline{RR'}\parallel\overline{SS'}\). 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.

Answer:

\(\overline{RR'}\parallel\overline{SS'}\)