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

Reflection is a rigid transformation. Rigid transformations (like reflection) preserve the lengths of the sides of a figure. That is, if a figure \(ABCD\) is reflected over a line \(y\) to get a figure \(TURS\), then the corresponding sides of \(ABCD\) and \(TURS\) are equal in length.

Step2: Identify the corresponding side

In the reflection of quadrilateral \(ABCD\) over line \(y\) to get quadrilateral \(TURS\), side \(AB\) in quadrilateral \(ABCD\) corresponds to side \(TU\) in quadrilateral \(TURS\).

Since \(AB = 7\) in, and because of the property of reflection (corresponding sides of congruent figures are equal), \(TU=AB\).

Answer:

\(7\) in.