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DesCartesian Division

DesCartesian Division
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2017-07-10 08:59
VectorCoordinate GeometryProbability & StatisticsGeometric Construction
This example demonstrates the relationship between division, rotation, correlation, hypergeometric distribution, and hyperbola within Cartesian coordinates and set theory. It involves core mathematical concepts like coordinate geometry, vectors, rotation, hypergeometric distribution, and hyperbolas. The construction uses commands such as Point, Intersect, Segment, Vector, Line, and Ray in GeoGebra. Suitable for high school students and mathematicians.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → O
  3. Segment(O, A) → a
  4. Point(yAxis) → B
  5. Segment(O, B) → b
  6. Segment(A, B) → d
  7. Vector(A, B) → u
  8. Vector(B, A) → v
  9. Point(yAxis) → C
  10. Segment(C, O) → f
  11. Line(C, v) → g
  12. Point(f) → D
  13. Point(xAxis) → E
  14. Ray(D, E) → h
  15. Intersect(g, h) → F
  16. Vector(C, F) → w
  17. Line(C, F) → i
  18. Line(C, v) → j
  19. Point(xAxis) → G
  20. Ray(A, G) → k
  21. Intersect(j, k) → H
  22. Segment(H, C) → l
  23. Vector(C, H) → c
  24. Segment(F, D) → m
  25. Segment(H, D) → n
  26. Segment(C, F) → p
  27. Segment(C, H) → q
  28. Point(v) → I
  29. Point(v) → J
  30. Segment(I, J) → r
  31. Segment(B, A) → s
  32. Point(r) → L
  33. Line(B, L) → t
  34. Line(H, C) → e
  35. Intersect(f, n) → M
  36. Line(C, F) → f_1

AI Drawing Prompt Reference

Draw a Cartesian coordinate system with point O at the origin, point A on the x-axis, and point B on the y-axis. Connect O and A to form segment a, connect O and B to form segment b, and connect A and B to form segment d. Vector u goes from A to B, and vector v goes from B to A. On the y-axis, take point C and connect C and O to form segment f. Draw line g through C in the direction of vector v. Point D is on the x-axis, and from D, draw ray h that intersects line g at point F. Vector w goes from C to F, and draw line i through C and F, and line j through C and v. On the x-axis, take point E, and from D, draw ray k that intersects line j at point H. Connect H and C to form segment l, vector c goes from C to H, connect F and D to form segment m, connect H and D to form segment n, connect C and F to form segment p, and connect C and H to form segment q. On vector v, take points I and J, and connect I and J to form segment r. Connect B and A to form segment s. Point L is on segment r, and from B, draw line t through L. From H, draw line e through C, and line e intersects segment f at point M. Draw line f_1 through C.
The prompt above was compiled from the original drawing commands and is for reference only.