Question

1. in the diagram, \\( \overleftrightarrow { s v } \\) is the perpendicular bisector of \\( \overline { r t } \\). because \\( u r = u t = 14 \\), what can you conclude about point \\( u \\)?

Explanation:

Step1: Recall the perpendicular bisector theorem

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Conversely, if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.

Step2: Apply the theorem to point \(U\)

Given that \(UR = UT=14\), by the converse of the perpendicular bisector theorem, since point \(U\) is equidistant from the endpoints \(R\) and \(T\) of segment \(\overline{RT}\), and \(\overleftrightarrow{SV}\) is the perpendicular bisector of \(\overline{RT}\).

Answer:

Point \(U\) lies on the perpendicular bisector \(\overleftrightarrow{SV}\) of \(\overline{RT}\).