Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. $overline{rs}$ is the perpendicular bisector of $overline{pq}$. point $t$ is the midpoint of $overline{pq}$. point $u$ lies on $overline{rs}$. if the length of $overline{up}$ is 7 units, the length of $overline{uq}$ is units.

Explanation:

Step1: Recall property of perpendicular bisector

Any point on the perpendicular bisector of a line - segment is equidistant from the endpoints of the line - segment.

Step2: Apply the property

Since $\overline{RS}$ is the perpendicular bisector of $\overline{PQ}$, and point $U$ lies on $\overline{RS}$, we have $UP = UQ$.
Given that $UP = 7$ units, so $UQ=7$ units.

Answer:

7