Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
in the figure, \\( \overline { c d } \\) is the perpendicular bisector of \\( \overline { a b } \\).
if the length of \\( \overline { a c } \\) is \\( 2 x \\) and the length of \\( \overline { b c } \\) is \\( 3 x - 5 \\), the value of \\( x \\) is

Explanation:

Step1: Recall perpendicular bisector property

A point on the perpendicular bisector of a segment is equidistant from the segment's endpoints. So, \( AC = BC \).

Step2: Set up the equation

Given \( AC = 2x \) and \( BC = 3x - 5 \), we set them equal: \( 2x = 3x - 5 \).

Step3: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 0 = x - 5 \). Then add 5 to both sides: \( x = 5 \).

Answer:

5