Question

identify the segment bisector of (overline{xy}).
diagram: point x, m, y on a line; line n intersects at m. xm labeled (5x + 8), my labeled (9x + 12). options: (overline{xm}), x, line n, (overline{ym}). the length of (overline{xy}) is...

Explanation:

Step1: Recall the definition of a segment bisector

A segment bisector is a line, ray, or segment that divides another segment into two equal parts. In the diagram, we see that line \( n \) intersects \( \overline{XY} \) at point \( M \), and the markings indicate that \( XM = MY \) (since \( 5x + 8 \) and \( 9x + 12 \) would be equal when \( M \) is the midpoint, but more importantly, the visual bisector here is line \( n \) as it passes through the midpoint \( M \) of \( \overline{XY} \)).

Step2: Analyze the options

• \( \overline{XM} \): This is a segment from \( X \) to \( M \), not a bisector (a bisector should pass through the midpoint and extend, or be a line/ray/segment that divides \( \overline{XY} \) into two equal parts; \( \overline{XM} \) is part of \( \overline{XY} \) or a segment from \( X \) to \( M \), not the bisector).
• \( X \): A point, not a bisector.
• Line \( n \): Passes through the midpoint \( M \) of \( \overline{XY} \), so it divides \( \overline{XY} \) into two equal parts (\( \overline{XM} \) and \( \overline{MY} \)), so it is the segment bisector.
• \( \overline{YM} \): Similar to \( \overline{XM} \), a segment from \( Y \) to \( M \), not the bisector.

Answer:

line \( n \)