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 (reflections, rotations, translations) preserve the lengths of segments. That is, if a figure \(ABCD\) is reflected over a line \(y\) to get a figure \(TURS\), then the corresponding sides of the two figures are equal.

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 \(TURS\).

Answer:

\(7\) in.