Question

identify the segment bisector of (overline{jk}).

line segment with points j, m, k. jm is labeled (7x + 5), mk is labeled (8x), with tick marks on jm and mk indicating they are equal.

options:

• (j)
• (m)
• (overline{jm})
• (overline{km})

the length of (overline{jm}) is (square).

Explanation:

Step1: Define segment bisector

A segment bisector divides a segment into two equal parts, so $JM = KM$.

Step2: Set up equation

Substitute the given expressions:
$7x + 5 = 8x$

Step3: Solve for $x$

Subtract $7x$ from both sides:
$8x - 7x = 5$
$x = 5$

Step4: Calculate length of $\overline{JM}$

Substitute $x=5$ into $7x+5$:
$7(5) + 5 = 35 + 5 = 40$

Step5: Identify bisector

Point $M$ divides $\overline{JK}$ into two equal segments, so $M$ is the segment bisector.

Answer:

M
The length of $\overline{JM}$ is 40