Question

identify the segment bisector of $overline{jk}$. the length of $overline{jm}$ is .

Explanation:

Step1: Recall bisector property

A segment bisector divides a segment into two equal - length parts. So, $JM = MK$. 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: $15 - 25=5x$, which gives $- 10 = 5x$. Divide both sides by 5: $x=-2$.

Step3: Find the length of $JM$

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

Step4: Identify the segment bisector

Since line $l$ passes through the mid - point $M$ of $\overline{JK}$, the segment bisector of $\overline{JK}$ is line $l$.

Answer:

C. line $l$
The length of $\overline{JM}$ is $9$