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By the Bay 2.0

By the Bay 2.0
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2020-06-03 22:03
FunctionCoordinate GeometryOptimization
This example demonstrates geometric shapes near a bay. Key mathematical concepts include functions, symmetry, and interval division. Using GeoGebra commands such as Line, Point, Intersect, etc., a dynamic geometric figure is constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(A, B) → g
  3. Point(g) → C
  4. Point(g) → D
  5. OrthogonalLine(C, g) → h
  6. Point(h) → drag_1
  7. OrthogonalLine(drag_1, h) → i
  8. Point(i) → drag_2
  9. OrthogonalLine(drag_2, i) → j
  10. Intersect(j, f) → G
  11. Segment(C, drag_1) → k
  12. Segment(drag_1, drag_2) → l
  13. Segment(drag_2, G) → m
  14. Polygon(C, drag_1, drag_2, G) → q1, c, e, f_1, g_1
  15. PointIn(q1) → Pointq1
  16. Midpoint(drag_1, C) → H
  17. Midpoint(drag_2, G) → I
  18. Midpoint(drag_1, drag_2) → J
  19. Midpoint(drag_1, G) → K

AI Drawing Prompt Reference

Draw a straight line and place two points on it. Through each point, construct a perpendicular line, and place a draggable point on each perpendicular. From each draggable point, draw another perpendicular to its own perpendicular line, creating two new lines; one of these new lines intersects the original line at a point. Connect the two original points, the two draggable points, and the intersection point in order to form a quadrilateral, and place a point inside it. Finally, mark the midpoints of the four sides of the quadrilateral. The figure shows a dynamic construction with a quadrilateral, an interior point, and several midpoints.
The prompt above was compiled from the original drawing commands and is for reference only.