Question

1. ac is 6 units long. point b is on ac. if ab=18x and bc=6x, a.) what is the value of x? b.) how long is line segment ab?

Explanation:

Part a)

Step1: Use segment addition postulate

Since \( B \) is on \( AC \), we have \( AB + BC = AC \). Substituting the given expressions, we get \( 18x + 6x = 6 \).

Step2: Combine like terms

Combine \( 18x \) and \( 6x \): \( 24x = 6 \).

Step3: Solve for \( x \)

Divide both sides by 24: \( x=\frac{6}{24}=\frac{1}{4} \).

Step1: Substitute \( x \) into \( AB \)

We know \( AB = 18x \) and \( x=\frac{1}{4} \), so substitute \( x \) into the expression: \( AB = 18\times\frac{1}{4} \).

Step2: Calculate the value

Simplify \( 18\times\frac{1}{4}=\frac{18}{4}=\frac{9}{2} = 4.5 \).

Answer:

\( x = \frac{1}{4} \)

Part b)