Question

the image of trapezoid pqrs after a reflection across wy is trapezoid pqrs. what is the relationship between rr and ss? rr = 2ss rr = 4ss rr || ss rr ⊥ 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 a point - image pair and points \(S\) and \(S'\) are a point - image pair with respect to the line of reflection \(\overleftrightarrow{WY}\).

Step2: Determine the relationship

Since the line segments joining points and their images (\(\overline{RR'}\) and \(\overline{SS'}\)) are both perpendicular to the line of reflection \(\overleftrightarrow{WY}\), we have \(\overline{RR'}\parallel\overline{SS'}\). There is no information given to suggest a length - multiple relationship between \(\overline{RR'}\) and \(\overline{SS'}\).

Answer:

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