Question

identify the segment bisector of $overline{rs}$ .
diagram with points r, m, s, line ( s ), and ( rm = 12 ) (marked with a midpoint symbol at ( m ) for ( overline{rs} ))
options: ( overline{ms} ), ( overline{rm} ), ( s ), line ( s )
the length of ( overline{rs} ) is ( square ).

Explanation:

Step1: Recall segment bisector definition

A segment bisector is a line, ray, or segment that divides a segment into two equal parts. From the diagram, line \( s \) (the line with the arrow) intersects \( \overline{RS} \) at \( M \), and the marks show \( RM = MS \) (since there are congruency marks on both sides of \( M \) on \( \overline{RS} \)). So line \( s \) bisects \( \overline{RS} \).

Step2: Analyze other options

• \( \overline{MS} \): This is a segment, not a bisector (the bisector here is the line through \( M \), not just the segment \( MS \)).
• \( \overline{RM} \): Similar to above, it's a segment, not the bisector.
• \( S \): This is a point, not a bisector.

Step1: Determine \( RM \) length

From the diagram, \( RM = 12 \).

Step2: Find \( RS \) length

Since \( M \) is the midpoint (because line \( s \) is the bisector), \( RS = RM + MS \) and \( RM = MS = 12 \). So \( RS = 12 + 12 = 24 \).

Answer:

line \( s \)

For the length of \( \overline{RS} \):