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First Degree Equation with Geometric Integration (Level 4)

First Degree Equation with Geometric Integration (Level 4)
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2016-04-11 06:28
PolygonFunctionCoordinate GeometryInequalityGeometric Construction
This GeoGebra example demonstrates solving first-degree equations (linear equations) in a dynamic geometry environment, integrating algebraic concepts with geometric figures. It involves core mathematical ideas such as linear equations, polygons, ellipses, conic sections, and perimeter calculations. The construction uses commands like Point, Polygon, Random, Textfield, If, Ellipse, Segment, Intersect, and Sequence to create multiple polygons (poly1, poly2, poly3, poly4), ellipses (f_1, etc.), text labels, and interactive buttons (Refresh, NewProblem) that generate random problems and link equations to visual shapes. Suitable for middle school to high school students for practicing equation solving and geometry, and useful for teachers in classroom demonstrations or for self-paced learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → E
  2. Polygon((10.455803599971945, 4.428079038697364), (11.45154195318282, 4.426628459182624), (11.45154195318282, 4.926628459182623), (10.455803599971945, 4.928079038697364)) → poly2, i, j, k, m
  3. Polygon(F, G, H, I) → poly3, f_1, g_1, h_1, i_1
  4. Polygon((-11.445852088028492, 4.308916490437969), (-10.445852088028493, 4.308916490437969), (-10.445852088028493, 4.8089164904379675), (-11.445852088028492, 4.8089164904379675)) → poly4, n, p, q, s
  5. Polygon((-10.543680266275816, -2.544527077316755), (-10.543680266275816, -1.5445270773167552), 4) → poly1
  6. Polygon((11.557939744940192, -2.5558711836942214), (11.557939744940192, -1.5558711836942218), 4) → poly1_3
  7. Random(1, 5) → u
  8. Random(2, 5) → ul1
  9. Random(1, 5) → l
  10. Random(1, 5) → ur
  11. Textfield(fml) → InputBox1
  12. Textfield(fmr) → InputFMR
  13. Textfield(fmul) → InputFMUL
  14. Textfield(fmur) → InputFMUR
  15. Textfield(dl) → InputBoxdl
  16. Textfield(dr) → Inputdr
  17. If((u * UL) + L ≟ (u * UR) + R, 0, If[(u * UL) + L ≥ (u * UR) + R, -1, 1]) → B
  18. If((u_2 * UL_2) ≟ R_2, 0, If[(u_2 * UL_2) ≥ R_2, -1, 1]) → B_2
  19. If((u_3 * UL_3) ≟ R_3, 0, If[(u_3 * UL_3) ≥ R_3, -1, 1]) → B_3
  20. If((u_1 * UL_1) ≟ R_1, 0, If[(u_1 * UL_1) ≥ R_1, -1, 1]) → B_1
  21. If((u_4 * UL_4) ≟ R_4, 0, If[(u_4 * UL_4) ≥ R_4, -1, 1]) → B_4
  22. Ellipse((-3, B), (-7, B), 2.25) → c_1
  23. Ellipse((3, (-B)), (7, (-B)), 2.25) → d_1
  24. Segment((-5, B_4), (-5, -3)) → a_1
  25. Intersect(c_1, a_1) → A_1,
  26. Segment((5, (-B_4)), (5, -3)) → b_1
  27. Intersect(d_1, b_1) → C_1,
  28. Segment(A_1, A'_1) → e_1
  29. Segment(C_1, C'_1) → f_2
  30. Segment(A'_1, C'_1) → g_2
  31. Intersect(g_2, yAxis) → A
  32. Segment(A, C) → b
  33. Sequence(Polygon[(-6.5, B - 1 + t), (-5.5, B - 1 + t), 4], t, 1, UL, 1) → list1
  34. Sequence(Polygon[(5.5, (-B) - 0.5 + t / 2), (6.5, (-B) - 0.5 + t / 2), (6.5, (-B) + t / 2), (5.5, (-B) + t / 2)], t, 1, R, 1) → list2
  35. Sequence(Polygon[(-4.5, B - 0.5 + t / 2), (-3.5, B - 0.5 + t / 2), (-3.5, B + t / 2), (-4.5, B + t / 2)], t, 1, L, 1) → list3
  36. Sequence(Polygon[(3.5, (-B) - 1 + t), (4.5, (-B) - 1 + t), 4], t, 1, UR, 1) → list4