Question

identify the segment bisector of $overline{xy}$.
3x + 1 8x - 24
x m y
n
o n
o x
$overrightarrow{mn}$
o $overline{my}$
the length of $overline{xy}$ is .

Explanation:

Step1: Recall bisector property

A segment bisector divides a segment into two equal - length parts. So, we set \(3x + 1=8x - 24\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(1 = 8x-3x - 24\), which simplifies to \(1 = 5x-24\). Then add 24 to both sides: \(1 + 24=5x\), so \(25 = 5x\). Divide both sides by 5, we get \(x = 5\).

Step3: Find length of \(XM\) or \(MY\)

Substitute \(x = 5\) into \(3x + 1\). \(XM=3\times5 + 1=15 + 1=16\).

Step4: Calculate length of \(XY\)

Since \(XY=XM + MY\) and \(XM = MY\), \(XY=2\times16 = 32\).

Answer:

32