Question

the image of trapezoid pqrs after a reflection across
w 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

When a figure is reflected over a line, the line segments connecting corresponding points (like \(RR'\) and \(SS'\)) are perpendicular to the line of reflection and parallel to each other.

Since \(RR'\) and \(SS'\) are both related to the reflection across \(\overleftrightarrow{W}\), by the property of reflection, \(\overline{RR'}\parallel\overline{SS'}\). There is no information in the reflection - transformation property that would make \(RR' = 2SS'\) or \(RR'=4SS'\) (unless there is a specific scale - factor which is not indicated here for a reflection, reflection is an isometric transformation). Also, \(\overline{RR'}\perp\overline{SS'}\) is incorrect as they are parallel (both are perpendicular to the line of reflection, and two lines perpendicular to the same line are parallel in a plane).

Answer:

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