Question

5.1 assignment
9 of 22
possible points: 0.45
perpendicular bisectors use the diagram below. \overleftrightarrow{jn} is the perpendicular bisector of \overline{mk}.
find kl.
(diagram with triangle or quadrilateral, labeled with expressions: 5y + 8, 7y - 5, 35, 7y + 1, 9y - 13 at various points j, k, m, l, n, p)
kl = \boxed{} units

Explanation:

Step1: Use the property of perpendicular bisector

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

Step2: Solve the equation for \( y \)

Subtract \( 5y \) from both sides: \( 7y-5y - 6=5y - 5y+ 8 \), which gives \( 2y-6 = 8 \).
Add \( 6 \) to both sides: \( 2y-6 + 6=8 + 6 \), so \( 2y=14 \).
Divide both sides by \( 2 \): \( y=\frac{14}{2}=7 \).

Step3: Find \( KL \)

Substitute \( y = 7 \) into the expression for \( KL \) (\( 7y + 1 \)).
\( KL=7\times7 + 1=49 + 1=50 \).

Answer:

\( 50 \)