Question

quadrilateral abcd is reflected over line segment y as shown, resulting in quadrilateral turs. if ad 5 in., ab = 7 in., dc = 4 in., and bc = 9 in., what is tu? 4 in 5 in. 7 in. 9 in. figure may not be drawn to scale.

Explanation:

Step1: Recall the property of reflection

A reflection is a rigid transformation. Rigid transformations (reflections, rotations, translations) preserve the lengths of segments.

Step2: Identify the corresponding segment

Quadrilateral \(ABCD\) is reflected over line \(y\) to get quadrilateral \(TURS\). The segment \(AB\) in quadrilateral \(ABCD\) corresponds to the segment \(TU\) in quadrilateral \(TURS\) (by the order of vertices in the name of the quadrilateral: \(A - B - C - D\) and \(T - U - R - S\)).
Since reflection preserves length, \(TU=AB\).

Answer:

\(7\) in.