Question

5.1 assignment
8 of 22
possible points: 0.45
perpendicular bisectors use the diagram below. \overleftrightarrow{jn} is the perpendicular bisector of \overline{mk}.
find jk.
(diagram with labels: jk = 5y + 8, jm = 7y - 5, mk segment with n and p, ml = 9y - 13, kl = 7y + 1, angle at n is right angle, length 35)
jk = \boxed{} units

Explanation:

Step1: Use the property of perpendicular bisector

Since \( \overrightarrow{JN} \) is the perpendicular bisector of \( \overline{MK} \), \( JM = JK \). So \( 5y + 8=7y - 6 \).

Step2: Solve the equation for \( y \)

Subtract \( 5y \) from both sides: \( 8 = 2y-6 \).
Add \( 6 \) to both sides: \( 14 = 2y \).
Divide both sides by \( 2 \): \( y = 7 \).

Step3: Find \( JK \)

Substitute \( y = 7 \) into \( JK=5y + 8 \).
\( JK=5\times7 + 8=35 + 8=43 \).

Answer:

\( 43 \)