Question

use the figure and the given information to find the indicated measure.
\\( \overleftrightarrow { z x } \\) is the perpendicular bisector of \\( \overline { w y } \\), \\( w z = 4 n - 13 \\), and \\( y z = n + 17 \\).
find \\( y z \\).
\\( y z = \square \\)

Explanation:

Step1: Use the property of perpendicular bisector

Since \( \overleftrightarrow{ZX}\) is the perpendicular bisector of \( \overline{WY}\), by the Perpendicular Bisector Theorem, \(WZ = YZ\).
So, \(4n-13=n + 17\).

Step2: Solve the equation for \(n\)

Subtract \(n\) from both sides: \(4n - n-13=n - n+ 17\), which simplifies to \(3n-13 = 17\).
Add \(13\) to both sides: \(3n-13 + 13=17 + 13\), so \(3n=30\).
Divide both sides by \(3\): \(n=\frac{30}{3}=10\).

Step3: Find \(YZ\)

Substitute \(n = 10\) into the formula for \(YZ\). Since \(YZ=n + 17\), then \(YZ=10 + 17\).

Answer:

\(27\)