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Signed Area and Determinant

Signed Area and Determinant
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2016-02-08 01:08
VectorCoordinate GeometryMatrix
This example illustrates the relationship between signed area and determinants. Key mathematical concepts include determinants, vectors, and geometric area. Using GeoGebra commands such as Vector, Line, Point, and Polygon, vectors and polygons are constructed to calculate the signed area. Suitable for high school mathematics education, particularly in coordinate geometry and linear algebra courses.

GeoGebra Commands & Parameters

  1. Vector(O, B) → u
  2. Vector(O, C) → v
  3. Line(C, u) → a
  4. Line(B, v) → b
  5. Point(a) → D
  6. Line(C, yAxis) → c
  7. Line(B, yAxis) → d
  8. Line(D, yAxis) → e
  9. Line(B, xAxis) → f
  10. Line(C, xAxis) → g
  11. Line(D, xAxis) → h
  12. Polygon(B, D, C, O) → poly1, b_1, d_1, c_1, a_1
  13. Intersect(h, yAxis) → E
  14. Intersect(c, h) → F
  15. Intersect(g, yAxis) → G
  16. Polygon(E, F, C, G) → poly2, e_1, f_1, c_2, g_1
  17. Intersect(d, xAxis) → H
  18. Intersect(e, xAxis) → I
  19. Intersect(e, f) → J
  20. Polygon(H, I, J, B) → poly3, h_1, i, j, b_2
  21. Polygon(B, J, D) → poly4, d_2, b_3, j_1
  22. Polygon(D, F, C) → poly5, c_3, d_3, f_2
  23. Polygon(O, H, B) → poly6, b_4, a_2, h_2
  24. Polygon(O, C, G) → poly7, g_2, a_3, c_4