1. **Problem:** Points A, B, and C are collinear. Given distances AB and BC, find AC. 2. **Formula:** Since points are collinear, the distance AC is the sum of AB and BC: $$AC = AB + BC$$ 3. **Part (a):** Given $AB=5$ and $BC=7$, calculate $AC$: $$AC = 5 + 7 = 12$$ 4. **Part (b):** Given $AB=7$ and $BC=10$, calculate $AC$: $$AC = 7 + 10 = 17$$ **Explanation:** When points lie on the same line, the total distance between the first and last point is the sum of the distances between intermediate points. This is because the points are arranged in a straight line without any gaps or overlaps. **Final answers:** - (a) $AC = 12$ - (b) $AC = 17$