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Parabolic Curves with Straight Lines

Parabolic Curves with Straight Lines
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2017-09-25 07:57
FunctionCoordinate GeometryTransformationGeometric ConstructionGraphing
This example demonstrates the relationship between parabolic curves and straight lines, focusing on geometric constructions. Key math concepts include parabola definition, line equations, rotation, reflection, and orthogonal lines. GeoGebra commands like Point, Segment, Rotate, Line, Mirror, and OrthogonalLine are used in the construction. Suitable for high school mathematics education to understand geometric transformations and locus problems in analytical geometry.

GeoGebra Commands & Parameters

  1. Point(Circle[A, n]) → B
  2. Segment(A, B) → f
  3. Rotate(A, 90°, C) → A'
  4. Point(Circle[A, n]) → D
  5. Segment(A, D) → g
  6. Point(Circle[A, n]) → E
  7. Segment(A, E) → h
  8. Rotate(E, 90°, C) → E'
  9. Segment(E, E') → j
  10. Line(C, yAxis) → k
  11. Mirror(E, k) → E'_1
  12. Mirror(E', k) → E''
  13. Segment(E'', E'_1) → l
  14. OrthogonalLine(C, k) → m
  15. Mirror(E'_1, m) → F
  16. Mirror(E'', m) → E'''
  17. Segment(E''', F) → p
  18. Mirror(E, m) → E'_2
  19. Mirror(E', m) → E''_1
  20. Segment(E'_2, E''_1) → q