Question

identify the segment bisector of $overline{xy}$. then find $xy$. 12. 13.

Explanation:

Step1: Identify the segment bisector

A segment bisector divides a line - segment into two equal parts. In both figures, the line \(l\) passing through point \(M\) is the segment bisector of \(\overline{XY}\) since it intersects \(\overline{XY}\) at its mid - point \(M\).

Step2: Calculate \(XY\) for the first figure

If \(MY = 7\), and \(M\) is the mid - point of \(\overline{XY}\), then \(XM=MY\). So \(XY=XM + MY\). Since \(XM = MY = 7\), \(XY=7 + 7=14\).

Step3: Calculate \(XY\) for the second figure

If \(XM = 9\), and \(M\) is the mid - point of \(\overline{XY}\), then \(XM=MY\). So \(XY=XM + MY\). Since \(XM = MY = 9\), \(XY=9 + 9 = 18\).

Answer:

For the first figure: The segment bisector is line \(l\), and \(XY = 14\).
For the second figure: The segment bisector is line \(l\), and \(XY = 18\).