**Question Stem:** 如图，A, B分别是数轴上的两点，点C为线段上任意一点，点M为AC的中点，点N为BC的中点，若点A, B表示的数分别为 a, b，那么 MN = (b - a) / 2. **Diagram Description:** * **Type:** Number line. * **Main Elements:** * A horizontal line labeled 'x' with an arrow indicating the positive direction. * Points A, M, C, N, B are marked on the line in that order from left to right. * Point 0 is marked on the line between M and C. * Point A is labeled with the coordinate 'a'. * Point B is labeled with the coordinate 'b'. **Other Relevant Text:** * **Hint/Explanation:** 本题主要考查了线段的和差, 线段的中点等知识点, 明确各线段间的关系是解题的关键。 由中点的定义可得: MC = 1/2 AC, CN = 1/2 BC, 再根据数轴上表示的数确定 AB, 然后再根据线段的和差及等量代换即可解答。 **Solution:** * **Steps:** * 解: ∵ 点 M 为 AC 的中点, 点 N 为 BC 的中点, * ∴ MC = 1/2 AC, CN = 1/2 BC, * ∵ 点 A, B 表示的数分别为 a, b, * ∴ AB = b - a * ∴ MN = MC + CN = 1/2 AC + 1/2 CB = 1/2 (AC + CB) = 1/2 AB = (b - a) / 2 * **Conclusion:** 故答案为: (b - a) / 2.