Question

ad is a perpendicular bisector of bc. find ac. 6x - 3, 3x + 6, ac = ?

Explanation:

Step1: Use Perpendicular Bisector Theorem

Since \( \overline{AD} \) is the perpendicular bisector of \( \overline{BC} \), by the Perpendicular Bisector Theorem, \( AB = AC \). So \( 6x - 3 = 3x + 6 \).

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 6x - 3x - 3 = 6 \) \( \Rightarrow 3x - 3 = 6 \).
Add 3 to both sides: \( 3x = 6 + 3 \) \( \Rightarrow 3x = 9 \).
Divide by 3: \( x = \frac{9}{3} = 3 \).

Step3: Find \( AC \)

Substitute \( x = 3 \) into \( AC = 3x + 6 \): \( AC = 3(3) + 6 = 9 + 6 = 15 \).

Answer:

\( 15 \)