Question

solving for an unknown segment length
what is the measure of ( overline{ac} )?
26 units
5 units
13 units
39 units

Explanation:

Step1: Set up equation

Since \(AB = BD\) (perpendicular bisector property), we have \(3x - 2=8x - 1\).

Step2: Solve for \(x\)

$$
LATEXBLOCK0
$$

This is wrong. Wait, no! Wait, actually, since \(AD = CD\) (given by the marks), so \(8x-1 = 6x + 9\).

Step2: Solve for \(x\) (correct equation)

$$
LATEXBLOCK1
$$

Step3: Find \(AC\)

Substitute \(x = 5\) into \(3x-2\) (since \(AB=3x - 2\) and \(AC = 2AB\) as \(AB\) is half of \(AC\) in the perpendicular - bisector - related triangle). \(AB=3\times5-2=13\), so \(AC = 2\times13=26\).

Answer:

26 units