请帮我讲解这道题目，针对初二学生，风格幽默有趣，适合短视频平台。---**Extraction Content:** **Question Stem:** 4. 如图，在平面直角坐标系中，AB⊥y轴，垂足为点B，将△ABO绕点A逆时针旋转到△AB₁O₁的位置，使点B的对应点B₁落在直线y = -³⁄₄x上，再将△AB₁O₁绕点B₁逆时针旋转到△A₁B₂O₂的位置，使点O₁的对应点O₂也落在直线y = -³⁄₄x上，如此下去，……，若点B的坐标为(0, 3)，则点B₃₇的坐标为( ). **Mathematical Formulas/Equations:** y = -³⁄₄x **Other Relevant Text:** 问题编号: 4. 坐标系类型: 平面直角坐标系. 初始条件: AB⊥y轴, 垂足为点B. 初始三角形: △ABO. 第一次变换: 将△ABO绕点A逆时针旋转到△AB₁O₁. 第一次条件: 点B的对应点B₁落在直线y = -³⁄₄x上. 第二次变换: 将△AB₁O₁绕点B₁逆时针旋转到△A₁B₂O₂. 第二次条件: 点O₁的对应点O₂落在直线y = -³⁄₄x上. 重复过程: 如此下去. 已知点B的坐标: (0, 3). 问题: 求点B₃₇的坐标. **Diagram Description:** * **Type:** Geometric figure in a Cartesian coordinate plane. * **Main Elements:** * **Coordinate Axes:** X-axis (labeled Ox) and Y-axis (labeled Oy) intersecting at the Origin (labeled O). * **Points:** O, A, B, A₁, B₁, O₁, A₂, B₂, O₂, A₃, B₃, O₃, O₄. Points O, O₁, O₂, O₃, O₄... and B₁, B₂, B₃... lie on a straight line extending from the origin into the second and third quadrants. Point B is on the positive Y-axis. Point A is on the positive X-axis. A₁, A₂, A₃ are positioned such that triangles AB₁O₁, A₁B₂O₂, A₂B₃O₃ are formed. * **Shapes:** Right triangles ABO, AB₁O₁, A₁B₂O₂, A₂B₃O₃ are shown. Triangle ABO has a right angle at B (implied by AB⊥y轴 and B on y-axis, A on x-axis assuming standard axis setup and O is the origin). The subsequent triangles are formed by rotations. * **Lines:** A straight line passes through the points O₁, O₂, O₃, O₄... and B₁, B₂, B₃, .... This line represents y = -³⁄₄x. Segment AB is shown perpendicular to the y-axis. * **Labels and Annotations:** Points are labeled O, A, B, O₁, A₁, B₁, O₂, A₂, B₂, O₃, A₃, B₃, O₄. Axes are labeled Ox and Oy. **Question:** 求点B₃₇的坐标. (Find the coordinates of point B₃₇.)