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 2x and the length of \\( \overline { b c } \\) is 3x - 5, the value of x is.

Explanation:

Step1: Use the property of perpendicular bisector

Since \(CD\) is the perpendicular bisector of \(AB\), then \(AC = BC\).
So, \(2x=3x - 5\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(2x-2x=3x - 5-2x\).
We get \(0=x - 5\).
Add \(5\) to both sides: \(x=5\).

Answer:

\(5\)