Question

use the figure and the given information to find the indicated measure. \overleftrightarrow{zx} is the perpendicular bisector of \overline{wy}, wz = 4n - 13, and yz = n + 17. find yz. yz = \square

Explanation:

Step1: Recall Perpendicular Bisector Property

Since \( \overleftrightarrow{ZX} \) is the perpendicular bisector of \( \overline{WY} \), any point on \( \overleftrightarrow{ZX} \) (here, point \( Z \)) is equidistant from \( W \) and \( Y \). So, \( WZ = YZ \).

Step2: Set Up the Equation

Given \( WZ = 4n - 13 \) and \( YZ = n + 17 \), set them equal:
\( 4n - 13 = n + 17 \)

Step3: Solve for \( n \)

Subtract \( n \) from both sides: \( 3n - 13 = 17 \)
Add 13 to both sides: \( 3n = 30 \)
Divide by 3: \( n = 10 \)

Step4: Find \( YZ \)

Substitute \( n = 10 \) into \( YZ = n + 17 \):
\( YZ = 10 + 17 = 27 \)

Answer:

\( 27 \)