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Position Vector of Triangle's Center of Gravity

Position Vector of Triangle's Center of Gravity
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2022-10-25 13:18
PolygonVectorGeometric Construction
This example demonstrates how to construct the position vector of a triangle's center of gravity using GeoGebra. Key math concepts include vectors, polygons, midpoints, segments, and intersections. The construction involves commands like Vector, Polygon, Midpoint, Segment, and Intersect, as outlined in the summary. It is suitable for middle school and above, focusing on geometric applications of centroids and vectors.

GeoGebra Commands & Parameters

  1. Vector(E, C) → u
  2. Vector(E, D) → v
  3. Vector(E, F) → w
  4. Polygon(C, D, F) → 다각형1, f, c, d
  5. Midpoint(c) → G
  6. Midpoint(d) → H
  7. Segment(G, C) → a
  8. Segment(D, H) → b
  9. Intersect(a, b) → I
  10. Vector(E, I) → z
  11. Midpoint(f) → J
  12. Segment(J, C) → h
  13. Segment(J, D) → i
  14. Segment(D, G) → j
  15. Segment(G, F) → k
  16. Segment(F, H) → m
  17. Segment(H, C) → n
  18. Segment(J, F) → q
  19. Segment(D, H) → r
  20. Vector(E, G) → w_1
  21. 도구1(C, I) → g_1
  22. 도구1(I, G) → h_1
  23. Polygon(C, E, G) → 다각형2, g_2, c_2, e_2
  24. Polygon(D, E, F) → 다각형3, f_1, d_2, e_3

AI Drawing Prompt Reference

Draw a triangle and its centroid's position vector. The triangle is formed by three points, and the centroid's position vector is determined by connecting the midpoints of the sides and finding their intersection. The construction order includes first determining the triangle vertices, then finding the midpoints of the sides, connecting the midpoints, and finally obtaining the centroid's position vector.
The prompt above was compiled from the original drawing commands and is for reference only.