Question

identify the segment bisector of \\(\overline{rs}\\).
image of a line segment rs with midpoint m, and a ray ma. the length from m to s is 9, and there are tick marks indicating mr and ms are equal. below the image are multiple-choice options: \\(\overrightarrow{ar}\\), \\(\overrightarrow{ma}\\) (selected), \\(\overline{mr}\\), \\(\overline{sm}\\). then a question: the length of \\(\overline{rs}\\) is \\(\square\\).

Explanation:

Step1: Define segment bisector

A segment bisector divides a segment into two equal parts, passing through its midpoint. From the diagram, $\overrightarrow{MA}$ passes through $M$, the midpoint of $\overline{RS}$, so it is the bisector.

Step2: Find length of $\overline{RS}$

Given $SM = 9$, and $MR = SM$ (since $M$ is the midpoint).
$\overline{RS} = MR + SM = 9 + 9$

Answer:

The segment bisector is $\boldsymbol{\overrightarrow{MA}}$
The length of $\overline{RS}$ is $\boldsymbol{18}$