1. **State the problem:** Points A, B, and C are collinear with B between A and C. Given $AB = 12$ and $AC = 19$, find $BC$. 2. **Formula and rule:** When three points are collinear and one point lies between the other two, the distances satisfy the segment addition postulate: $$AC = AB + BC$$ 3. **Apply the formula:** Substitute the known values: $$19 = 12 + BC$$ 4. **Solve for $BC$:** $$BC = 19 - 12$$ 5. **Calculate:** $$BC = 7$$ **Answer:** The length of segment $BC$ is 7.