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Open Middle: Triangle Area Problem (V2)

Open Middle: Triangle Area Problem (V2)
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2022-09-14 03:03
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates exploring the relationship between triangle area and coordinates, linear equations, and trigonometric functions by dynamically adjusting vertex coordinates. Core concepts include area calculation, coordinate geometry, and linear equations. GeoGebra commands like PointIn, Polygon, Segment, etc., are used in construction. Suitable for high school mathematics teaching, focusing on analytical geometry and function graphing exploration.

GeoGebra Commands & Parameters

  1. PointIn(e) → A
  2. PointIn(l(x, y) ∧ x ≥ x(A)) → C
  3. PointIn(j) → B
  4. Polygon(A, C, B) → t1, b_1, a_1, c_1
  5. Segment(A, B) → f
  6. Segment(B, C) → g
  7. Segment(C, A) → h
  8. SurdText(f) → text1
  9. SurdText(g) → text2
  10. SurdText(h) → text3
  11. SurdText(t1) → text4
  12. Mode(l1) → l2
  13. Length(l2) → i
  14. If(i ≟ 0, "No coordinates repeat!", "You have repeated coordinates.") → text5
  15. Intersect(p, eq1) → D
  16. Intersect(eq1, q) → E
  17. Intersect(q, eq2) → F
  18. Intersect(eq2, r) → G
  19. Polygon(A, G, C) → t2, c_2, a_2, g_1
  20. Polygon(A, F, B) → t4, b_2, a_4, f_1
  21. Intersect(eq3, p) → H
  22. Polygon(B, H, A) → t5, a_5, b_3, h_1
  23. Polygon(B, E, C) → t6, c_4, b_4, e_1
  24. Intersect(r, eq3) → I
  25. Polygon(B, I, C) → t7, c_5, b_5, i_1

AI Drawing Prompt Reference

Draw a triangle with adjustable vertex coordinates to show the relationship between triangle area and coordinates. The figure should include triangles, line segments, and text labels to illustrate area calculation and coordinate geometry concepts.
The prompt above was compiled from the original drawing commands and is for reference only.