Question

1. points a, b, and c are collinear and b is between a and c. given ab = 12 and ac = 19, what is bc?

Explanation:

Step1: Recall the segment addition postulate

Since points \( A \), \( B \), and \( C \) are collinear with \( B \) between \( A \) and \( C \), the segment addition postulate states that \( AB + BC = AC \).

Step2: Solve for \( BC \)

We know \( AB = 12 \) and \( AC = 19 \). Substitute these values into the equation \( AB + BC = AC \), we get \( 12 + BC = 19 \). To find \( BC \), subtract \( 12 \) from both sides of the equation: \( BC = AC - AB = 19 - 12 \).

Step3: Calculate the result

\( 19 - 12 = 7 \).

Answer:

\( 7 \)