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Open Middle: Slope and Points Exercise

Open Middle: Slope and Points Exercise
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2021-09-07 08:26
函数解析几何几何作图滑块动画函数图像
所属专题 Slope
This interactive GeoGebra exercise is designed to help students explore the concept of slope through point coordinates. It presents a coordinate plane with multiple points and lines, where students must adjust or select points to satisfy given slope conditions. The core mathematical concepts include coordinate geometry, slope definition (Δy/Δx), linear equations, and point-line relationships. The construction uses GeoGebra commands such as Polygon, If, Intersect, Line, Min, nCr, and Segment, creating multiple point objects (A, B, C, H, P, etc.) and line objects (f, g, h, i, etc.), with dynamic updates via conditional logic and intersection calculations. This resource is suitable for middle school to high school students learning analytic geometry and linear functions, particularly in an Open Middle format that encourages multiple solution paths and critical thinking.

GeoGebra 命令及参数

  1. Polygon(A0, B, 4) → poly0, f, g, h, i, A, C
  2. Polygon(A3, H, 4) → poly3, j, k, l, m, E, G
  3. Polygon(A7, P, 4) → poly7, n, p, q, r, I, K
  4. Polygon(A1, D, 4) → poly1, s, t, a, b, M, O
  5. Polygon(A6, N, 4) → poly6, c, d, e, f_1, Q, S
  6. Polygon(A2, H2, 4) → poly2, k_1, l_1, m_1, n_1, W, Z
  7. Polygon(A8, A8 + (2, 0), 4) → poly8, g_1, h_1, i_1, j_1, U, V
  8. Polygon(A9, T, 4) → poly9, p_1, q_1, r_1, s_1, A_1, B_1
  9. Polygon(A4, J, 4) → poly4, t_1, a_1, b_1, c_1, C_1, D_1
  10. Polygon(A5, L, 4) → poly5, d_1, e_1, f_2, g_2, E_1, F_1
  11. Polygon(K_1, L_1, 4) → poly10, l_2, m_2, n_2, p_2, M_1, N_1
  12. Polygon(O_1, P_1, 4) → poly12, q_2, r_2, s_2, t_2, Q_1, R_1
  13. Polygon(S_1, T_1, 4) → poly13, a_2, b_2, c_2, d_2, U_1, V_1
  14. Polygon(C_2, D_2, 4) → poly15, i_3, j_3, k_3, l_3, E_2, F_2
  15. Polygon(G_2, H_2, 4) → poly16, m_3, n_3, p_3, q_3, I_2, J_2
  16. Polygon(G_{3}, H_{3}, 4) → poly17, m_{4}, n_{4}, p_{4}, q_{4}, I_{3}, J_{3}
  17. Polygon(C_{3}, D_{3}, 4) → poly14, i_{4}, j_{4}, k_{4}, l_{4}, E_{3}, F_{3}
  18. If(aleft > aright, "Left side is bigger.", aleft < aright, "Right side is bigger", "Both sides are equal!") → text9
  19. Intersect(h_2, eq1) → R_2
  20. Intersect(f_3, eq2) → S_2
  21. Polygon(A_2, B_2, R_2) → t1, i_2, j_2, k_2
  22. Polygon(A_2, B_2, S_2) → t2, e_2, g_3, h_3
  23. Line(A_2, B_2) → r_3
  24. Min(y(A_2), y(B_2)) → o
  25. If(o ≟ y(A_2), t1, t2) → t3
  26. nCr(4, 2) → w
  27. Segment((-13.5, 9.5), (-10.5, 9.5)) → s_3
  28. Segment((-13.5, 3.5), (-10.5, 3.5)) → t_3
  29. Segment((-5.5, 9.5), (-2.5, 9.5)) → a_3
  30. If(o_1 ≟ 0, p15 / p10, ((-p15)) / p10) → u_2
  31. If(u_1 ≟ 0, p12 / p13, ((-p12)) / p13) → v_2
  32. If(w_1 ≟ 0, p17 / p14, ((-p17)) / p14) → w_2
  33. If(o_2 ≟ 0, p16, (-p16)) → b_3

AI 绘图提示语参考

在坐标平面上绘制多个四边形，使它们通过可移动的顶点形成不同的几何构造。在平面上标记若干控制点，分别连接成四边形线条，并在适当位置添加水平或垂直方向的线段。建立条件逻辑关系，根据某些点的坐标数值大小比较显示对应的文字说明（如“左边更大”、“右边更大”或“两边相等”）。通过交点命令计算特定线条的交点坐标，并基于这些交点进一步构造新的四边形区域。整个图形应体现坐标几何、斜率概念以及点线之间的动态关系，适合展示函数与几何的交互。
以上提示语为根据原始绘图命令整理而来，仅供参考。