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Reverse Tilted Duct Collecting Rain Water

Reverse Tilted Duct Collecting Rain Water
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2018-02-07 23:23
VectorFunctionGeometric Construction
In collections Rate & Accumulation Yr 4 Much&Fast
This example demonstrates a geometric model of a reverse tilted duct collecting rain water. It involves core mathematical concepts such as functions, 2D vectors, piecewise functions, and the Pythagorean theorem. The construction utilizes GeoGebra commands like Rotate, Angle, Ray, Circle, Intersect, OrthogonalLine, Segment, Line, Point, Polygon, Vector, and Text. It is suitable for high school students learning functions, vectors, and geometric constructions.

GeoGebra Commands & Parameters

  1. Rotate(A, α, B) → A'
  2. Angle(A, B, A') → β
  3. Ray(B, A) → a
  4. Ray(B, A') → b
  5. Circle(B, 5) → c
  6. Intersect(c, a) → C,
  7. OrthogonalLine(C, b) → d
  8. Intersect(b, d) → D
  9. Segment(B, D) → e
  10. Segment(D, C) → f
  11. Segment(C, B) → g
  12. OrthogonalLine(B, g) → h
  13. OrthogonalLine(C, g) → i
  14. Line(B, d) → j
  15. Line(D, xAxis) → k
  16. Point(j) → E
  17. Point(d) → F
  18. Ray(D, F) → l
  19. Ray(B, E) → m
  20. Point(h) → G
  21. Point(i) → H
  22. Polygon(G, B, C, H) → poly1, g_1, b_1, c_1, h_1
  23. Vector(K, L) → u
  24. Vector(M, N) → v
  25. Vector(O, P) → w
  26. Text(T) → text4

AI Drawing Prompt Reference

Draw a reverse tilted duct collecting rain water model. Start by rotating point A around point B to get point A', then calculate the angle β between A and A'. Draw two rays a and b from B, passing through A and A' respectively. Draw a circle c with B as the center and a radius of 5, intersecting ray a to get point C. Draw a perpendicular line d from C to ray b, intersecting ray b to get point D. Connect BD, DC, and CB to form a triangle. Then, draw a perpendicular line from D to CB, intersecting the x-axis to get point E, and draw a perpendicular line from D to line d to get point F. Draw a ray from F, intersecting the ray from D to get point G, and draw a perpendicular line from G to get point H. Connect GH, GB, and HC to form a triangle. Finally, draw vectors u, v, and w, and add text annotations in appropriate positions.
The prompt above was compiled from the original drawing commands and is for reference only.