Question

1. line l is the segment bisector of jk. find mk

(diagram: segment jk with midpoint m, line l intersecting at m; jm labeled ( 3x + 15 ), mk labeled ( 8x + 25 ))

Explanation:

Step1: Set JM = MK (Segment Bisector)

Since line \( l \) is the segment bisector of \( JK \), \( JM = MK \). So we set \( 3x + 15 = 8x + 25 \).

Step2: Solve for x

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

Step3: Find MK

Substitute \( x = -2 \) into \( MK = 8x + 25 \).
\( MK = 8(-2) + 25 = -16 + 25 = 9 \).

Answer:

\( 9 \)