帮我详细讲解图片中的数学题---**Question Number:** 24 **Question Stem:** 如图, 在平面直角坐标系中, 点 A、B 的坐标分别为 (a, 0), (0, b). 且 $|a-2b|+\sqrt{8-b}=0$. 将点 B 向右平移 4 个单位长度得到 C. (1) 求 A、B 两点的坐标; (2) 点 P、Q 分别为线段 BC、OA 两个动点, P 自 B 点向 C 点以 2 个单位长度/秒向右运动, 同时点 Q 自 A 点向 O 点以 4 个单位长度/秒向左运动, 设运动的时间为 t, 连接 PQ. 当 PQ 恰好平分四边形 BOAC 的面积时, 求 t 的值; (3) 点 D 是直线 AC 上一点, 连接 QD, 作 ∠QDE = 120°, 边 DE 与 BC 的延长线相交于点 E, DM 平分 ∠CDE, DN 平分 ∠ADQ, 当点 Q 运动时, ∠MDN 的度数是否变化? 请说明理由. **Diagram Description:** The image contains two coordinate plane diagrams. Both show the origin O at the intersection of the X and Y axes. **Upper Diagram:** * **Type:** Coordinate Plane Diagram. * **Axes:** X-axis (horizontal), Y-axis (vertical), Origin O at (0,0). * **Points:** O (origin), A on the positive X-axis, B on the positive Y-axis, C to the right of B (higher than A, to the right of B's x-coordinate), P on the segment BC. * **Lines/Segments:** OB (along Y-axis), OA (along X-axis), BC, AC. PQ is connected in the lower diagram, not explicitly shown as connected in the upper one, but implied by question (2). * **Shape:** Four points O, B, C, A forming a quadrilateral BOAC. This appears to be a parallelogram based on the shape and problem context of translation. * **Labels/Annotations:** Points O, B, P, C, A are labeled. Curly braces are drawn indicating movement along BC and OA, suggesting P moves along BC and Q (implied from the question, but not shown in this specific diagram) moves along OA. **Lower Diagram:** * **Type:** Coordinate Plane Diagram. * **Axes:** X-axis (horizontal), Y-axis (vertical), Origin O at (0,0). * **Points:** O (origin), B on the Y-axis, C to the right of B, A on the X-axis, P on BC, Q on OA. * **Lines/Segments:** OB, OA, BC, AC, PQ. * **Labels/Annotations:** Points O, B, P, C, Q, A are labeled. Arrows indicate the direction of movement: P from B towards C (right), Q from A towards O (left). **Title below the lower diagram:** (备用图) which translates to (Spare diagram).