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Land Plot Geometry Construction

Land Plot Geometry Construction
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2019-05-07 13:40
VectorFunctionCoordinate GeometryCalculusGeometric Construction
This example demonstrates the process of constructing complex geometric figures using basic elements like points, lines, polygons, and circles. It involves core math concepts including coordinate geometry, vectors, derivatives, quadratic functions, and limits. GeoGebra commands such as OrthogonalLine, Point, Intersect, Polygon, Segment, Circle, and Vector are used in the construction. Suitable for high school and above students to learn geometric constructions, function graphs, and applications of calculus.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A_1, xAxis) → a
  2. OrthogonalLine(A_1, yAxis) → b
  3. Point(b) → B
  4. Point(a) → C
  5. OrthogonalLine(C, a) → c
  6. OrthogonalLine(B, c) → d
  7. Intersect(c, d) → D
  8. Polygon(A_1, B, D, C) → poly1, a_1, b_1, d_1, c_1
  9. Point(a_1) → A
  10. Segment(A, B) → e
  11. Circle(C, e) → f
  12. Intersect(f, a, 1) → F
  13. OrthogonalLine(F, a) → g
  14. OrthogonalLine(A, a_1) → h
  15. Intersect(g, h) → G
  16. Polygon(A_1, A, G, F) → poly2, a_2, e_1, g_1, f_1
  17. Intersect(xAxis, yAxis) → H
  18. Point(xAxis) → I
  19. Vector(H, I) → u
  20. Point(yAxis) → J
  21. Vector(H, J) → v
  22. Intersect(b_1, a_1) → L

AI Drawing Prompt Reference

Please draw a geometric figure composed of points, line segments, and circles. First, draw a line perpendicular to the x-axis from the origin, then draw a line perpendicular to the y-axis. Then, mark the intersection of these two lines as B, and mark the intersection of the line perpendicular to the x-axis and the line perpendicular to the y-axis as C. Next, draw a line c perpendicular to C and a line d perpendicular to B, and find their intersection D. Then, use points A1, B, D, C to form a polygon. Next, draw a line segment e from A1 to B, and draw a circle f centered at C with radius e. Find the intersection F of circle f with line a. Then, draw a line g perpendicular to F and a line h perpendicular to A1, and find their intersection G. Then, use points A1, A, G, F to form another polygon. Finally, find the intersection H of the x-axis and y-axis, and draw vectors u and v from H. Ensure that the figure includes these key objects and their relationships.
The prompt above was compiled from the original drawing commands and is for reference only.