Question

identify the segment bisector of $overline{rs}$. the length of $overline{rs}$ is

Explanation:

Step1: Recall segment - bisector definition

A segment bisector is a line, ray, or segment that divides a line segment into two equal parts. Here, line \(k\) intersects segment \(\overline{RS}\) at point \(M\) and divides it into two parts.

Step2: Identify the bisector

Since line \(k\) intersects \(\overline{RS}\) at \(M\) and splits \(\overline{RS}\) into two segments \(\overline{RM}\) and \(\overline{MS}\), the segment bisector of \(\overline{RS}\) is line \(k\).

Step3: Calculate the length of \(\overline{RS}\)

Given \(\overline{RM}=17\), and because \(M\) is the mid - point (due to line \(k\) being the bisector), \(\overline{MS}=\overline{RM} = 17\). So, \(RS=RM + MS=17 + 17=34\).

Answer:

The segment bisector of \(\overline{RS}\) is line \(k\). The length of \(\overline{RS}\) is \(34\).