讲解本题---**Question Stem:** 24. (14 分) 如图 1, 在平面直角坐标系中, A (a, 0), B (b, 3), C (4, 0), 且满足 $(a+b)^2 + |a-b+6| = 0$, 线段 AB 交 y 轴于 F 点. **Mathematical Formula:** $(a+b)^2 + |a-b+6| = 0$ **Sub-questions:** (1) 求点 A、B 的坐标. (2) 点 D 为 y 轴正半轴上一点, 若 ED || AB, 且 AM, DM 分别平分 ∠CAB, ∠ODE, 如 图 2, 求 ∠AMD 的度数. (3) 如 图 3, (也可以利用图 1) ① 求点 F 的坐标; ② 点 P 为坐标轴上一点, 若 △ABP 的三角形和 △ABC 的面积相等? 若存在, 求出 P 点坐标. **Chart/Diagram Descriptions:** **图 1 (Figure 1):** * Type: Coordinate plane diagram illustrating points and lines. * Main Elements: * Coordinate Axes: X-axis (labeled 'x') and Y-axis (labeled 'y') intersecting at the origin O. Arrowheads indicate positive directions. * Points: A, O, C are on the x-axis. B is in the first quadrant. F is on the y-axis. * Lines/Segments: Line segment AB intersects the y-axis at F. Line segments AC and BC form a triangle ABC. AC lies on the x-axis. **图 2 (Figure 2):** * Type: Coordinate plane diagram with additional points and lines relative to Figure 1. * Main Elements: * Coordinate Axes: X-axis (labeled 'x') and Y-axis (labeled 'y') intersecting at the origin O. Arrowheads indicate positive directions. * Points: A, O, C on the x-axis. B in the first quadrant. F on the y-axis. D is on the positive y-axis. E and M are other points. * Lines/Segments: Line segment AB intersects the y-axis at F. Line segment AC on the x-axis. Line segment BC. Line segment ED. Line segment DM. Line segment AM. OD is on the y-axis. OC is on the x-axis. * Lines: ED is parallel to AB. AM is the angle bisector of ∠CAB. DM is the angle bisector of ∠ODE. **图 3 (Figure 3):** * Type: Coordinate plane diagram similar to Figure 1, illustrating points and lines. * Main Elements: * Coordinate Axes: X-axis (labeled 'x') and Y-axis (labeled 'y') intersecting at the origin O. Arrowheads indicate positive directions. * Points: A, O, C on the x-axis. B in the first quadrant. F is on the y-axis. * Lines/Segments: Line segment AB intersects the y-axis at F. Line segments AC and BC form a triangle ABC. AC lies on the x-axis.