Question

if k is the midpoint of line segment jl, ( jk = 8x + 11 ) and ( kl = 14x - 1 ), find ( jk ).
options:
( \boldsymbol{\text{a}} ) ( jk = 8 )
( \boldsymbol{\text{b}} ) ( jk = 34 )
( \boldsymbol{\text{c}} ) ( jk = 2 )
( \boldsymbol{\text{d}} ) ( jk = 27 )

Explanation:

Step1: Use midpoint property

Since K is the midpoint of JL, \( JK = KL \). So we set up the equation:
\( 8x + 11 = 14x - 1 \)

Step2: Solve for x

Subtract \( 8x \) from both sides:
\( 11 = 6x - 1 \)
Add 1 to both sides:
\( 12 = 6x \)
Divide both sides by 6:
\( x = 2 \)

Step3: Find JK

Substitute \( x = 2 \) into \( JK = 8x + 11 \):
\( JK = 8(2) + 11 = 16 + 11 = 27 \)

Answer:

D. \( JK = 27 \)