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Explanation of Line Equations Through the Origin

Explanation of Line Equations Through the Origin
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2019-02-19 07:42
FunctionTrigonometryCoordinate Geometry
This example demonstrates the equations of lines passing through the origin. Key mathematical concepts include linear equations and slope. Using GeoGebra commands such as Intersect, Point, Rotate, etc., different lines with varying slopes can be constructed. Suitable for students in middle school and above to learn about linear equations and slope.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Rotate(B, α, A) → B'
  4. Angle(B, A, B') → β
  5. Point(yAxis) → C
  6. Line(C, xAxis) → f
  7. Circle(C, a) → c
  8. Intersect(c, f) → D, E
  9. OrthogonalLine(E, f) → g
  10. Point(yAxis) → F
  11. Line(F, f) → h
  12. Intersect(g, h) → G
  13. Polygon(C, F, G, E) → q1, c_1, f_1, g_1, e
  14. Line(A, B') → i
  15. OrthogonalLine(A, i) → j
  16. Circle(A, 0.8) → d
  17. Intersect(d, j, 2) → H
  18. Line(H, i) → k
  19. Circle(H, 0.4) → p
  20. Intersect(p, j, 2) → I
  21. Line(I, k) → l
  22. Circle(I, 0.4) → q
  23. Intersect(q, j, 2) → J
  24. Line(J, l) → m
  25. Circle(H, (b * a)) → r
  26. Intersect(r, k, 2) → K
  27. OrthogonalLine(K, k) → n
  28. Intersect(l, n) → L
  29. Polygon(H, K, L, I) → q2, h_1, k_1, l_1, i_1
  30. Intersect(g, n) → M
  31. Line(A, M) → s
  32. Circle(J, a) → t
  33. Intersect(t, m, 2) → N
  34. Circle(N, a) → d_1
  35. Intersect(d_1, m, 2) → O
  36. Circle(O, a) → e_1
  37. Intersect(e_1, m, 2) → P
  38. Circle(P, a) → p_1
  39. Intersect(p_1, m, 2) → Q
  40. Circle(Q, a) → q_1
  41. Intersect(q_1, m, 2) → R
  42. Circle(R, a) → r_1
  43. Intersect(r_1, m, 2) → S
  44. Circle(S, a) → s_1
  45. Intersect(s_1, m, 2) → T
  46. Circle(T, a) → t_1
  47. Intersect(t_1, m, 2) → U
  48. Circle(U, a) → c_2
  49. Intersect(c_2, m, 2) → V
  50. Circle(V, a) → d_2
  51. Intersect(d_2, m, 2) → W
  52. Intersect(m, n) → Z
  53. Ray(J, Q) → j_1