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Vector and Linear Function Interaction Demo

Vector and Linear Function Interaction Demo
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2019-02-13 21:18
VectorFunctionCoordinate GeometryGeometric Construction
①This example demonstrates the interaction between vectors, linear functions, and geometric shapes, dynamically constructing to show slope, distance, and rotation effects; ②Core mathematical concepts include vector operations, linear functions, slope calculation, geometric transformations, and distance formulas; ③Construction highlights are derived from the construction summary, using commands/objects like Line (straight line), Point (point), Ray (ray), Circle (circle), Intersect (intersection), Segment (segment), Distance (distance), If (conditional), Zip (combination), Rotate (rotation) in GeoGebra; ④Suitable for high school mathematics teaching, helping students understand the connection between vectors, functions, and geometry, enhancing spatial imagination and dynamic geometric analysis skills.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → a
  2. Point(a) → B
  3. Ray(A, B) → e
  4. Point(e) → C
  5. Circle(A, C) → d
  6. Intersect(d, a, 1) → D
  7. Segment(D, C) → f
  8. Distance(A, C) → AC
  9. If(Ms ≟ "", Sequence[(p, y(A) + 0.2), p, x(A) + OneDiv10, x(A) + AC - OneDiv10, OneDiv10], Sequence[(q, y(A) + 0.2), q, x(A) - OneDiv10, x(A) - AC + OneDiv10, 0 - OneDiv10]) → ListTop
  10. If(Ms ≟ "", Sequence[(p, y(A) - 0.2), p, x(A) + OneDiv10, x(A) + AC - OneDiv10, OneDiv10], Sequence[(q, y(A) - 0.2), q, x(A) - OneDiv10, x(A) - AC + OneDiv10, 0 - OneDiv10]) → ListBottom
  11. Zip(Segment[p, q], p, ListTop, q, ListBottom) → ScaleSeg
  12. If(Ms ≟ "", (x(A) + (b * OneDiv10) + (c * OneDiv100), y(A)), (x(A) - (b * OneDiv10) - (c * OneDiv100), y(A))) → E
  13. If(Ms ≟ "", Sequence[(p, y(A) - 0.15), p, x(A) + (b * OneDiv10) + OneDiv100, x(A) + ((b + 1) * OneDiv10) - OneDiv100, OneDiv100], Sequence[(q, y(A) - 0.15), q, x(A) - (b * OneDiv10) - OneDiv100, x(A) - ((b + 1) * OneDiv10) + OneDiv100, 0 - OneDiv100]) → ListBottomS
  14. If(Ms ≟ "", Sequence[(p, y(A) + 0.15), p, x(A) + (b * OneDiv10) + OneDiv100, x(A) + ((b + 1) * OneDiv10) - OneDiv100, OneDiv100], Sequence[(q, y(A) + 0.15), q, x(A) - (b * OneDiv10) - OneDiv100, x(A) - ((b + 1) * OneDiv10) + OneDiv100, 0 - OneDiv100]) → ListTopS
  15. Zip(Segment[p, q], p, ListTopS, q, ListBottomS) → ScaleSegS
  16. Segment((x(E), y(E) + 0.4), (x(E), y(E) - 0.4)) → g
  17. Circle(C, 1) → k
  18. Intersect(k, a, 2) → F
  19. Circle(F, 0.4) → p
  20. Intersect(p, a, 1) → G
  21. Rotate(G, 30°, F) → G'
  22. Rotate(G, (-(30°)), F) → G'_1
  23. Segment(F, G'_1) → j
  24. Segment(F, G') → l
  25. Segment(C, F) → m
  26. Circle(D, 1) → q
  27. Intersect(q, a, 1) → H
  28. Circle(H, 0.4) → r
  29. Intersect(r, a, 2) → I
  30. Rotate(I, 30°, H) → I'
  31. Rotate(I, (-(30°)), H) → I'_1
  32. Segment(I'_1, H) → n
  33. Segment(H, I') → s
  34. Segment(H, D) → t