Question

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

Explanation:

Step1: Recall segment - bisector definition

A segment bisector is a line, ray, or segment that divides a line segment into two equal parts. In the given figure, line \(k\) intersects segment \(\overline{RS}\) at its mid - point \(M\).

Step2: Analyze the options

• \(\overline{RM}\) and \(\overline{MS}\) are segments that are the result of the bisection, not the bisector itself. Point \(S\) is an endpoint of the segment \(\overline{RS}\), not a bisector. Line \(k\) is the line that divides \(\overline{RS}\) into two equal parts \(\overline{RM}\) and \(\overline{MS}\).

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

Since \(M\) is the mid - point of \(\overline{RS}\) and \(RM = 17\), then \(RS=2\times RM\). So \(RS = 2\times17=34\).

Answer:

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