Question

points a, b, and c are collinear. point b is between a and c. find the length indicated. 9) find ac if ab = 16 and bc = 12. 10) find ac if ab = 13 and bc = 9.

Explanation:

Problem 9:

Step1: Understand collinear points

Since \( A \), \( B \), \( C \) are collinear and \( B \) is between \( A \) and \( C \), we use the segment addition postulate: \( AC = AB + BC \).

Step2: Substitute values

Given \( AB = 16 \) and \( BC = 12 \), substitute into the formula: \( AC = 16 + 12 \).

Step3: Calculate the sum

\( 16 + 12 = 28 \).

Step1: Apply segment addition postulate

As \( A \), \( B \), \( C \) are collinear with \( B \) between \( A \) and \( C \), \( AC = AB + BC \).

Step2: Substitute given values

Given \( AB = 13 \) and \( BC = 9 \), substitute: \( AC = 13 + 9 \).

Step3: Compute the result

\( 13 + 9 = 22 \).

Answer:

\( AC = 28 \)

Problem 10: