Question

identify the segment bisector of $overline{jk}$. 8 o $overline{jm}$ o $j$ o line $l$ o $overline{km}$ the length of $overline{jm}$ is

Explanation:

Step1: Recall segment - bisector definition

A segment bisector divides a line - segment into two equal parts. So, if line \(l\) is the bisector of \(\overline{JK}\), then \(JM = MK\). Set up the equation \(3x + 15=8x + 25\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(15 = 5x+25\). Then subtract 25 from both sides: \(15 - 25=5x\), so \(- 10 = 5x\). Divide both sides by 5: \(x=-2\).

Step3: Find the length of \(JM\)

Substitute \(x = - 2\) into the expression for \(JM\): \(JM=3x + 15=3\times(-2)+15=-6 + 15 = 9\).

Step4: Identify the segment bisector

Since line \(l\) intersects \(\overline{JK}\) at its mid - point \(M\), the segment bisector of \(\overline{JK}\) is line \(l\).

Answer:

The segment bisector of \(\overline{JK}\) is line \(l\). The length of \(JM\) is \(9\).