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Parabola by Geometric Definition with GeoGebra

Parabola by Geometric Definition with GeoGebra
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2015-03-20 11:31
Coordinate GeometryOptimizationGeometric Construction
This example demonstrates the geometric definition of a parabola using GeoGebra. Key math concepts involved include geometric mean, area, line segment, and optimization problems. Construction highlights the use of GeoGebra commands like Line, Point, Segment, LineBisector, OrthogonalLine, Intersect, Distance, and objects such as A, B, a, C, D, b, c, d, E, CE, distanceDE, TextDE, e. Suitable for high school and above learning coordinate geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Point(a) → D
  3. Segment(C, D) → b
  4. LineBisector(b) → c
  5. OrthogonalLine(D, a) → d
  6. Intersect(c, d) → E
  7. Segment(C, E) → CE
  8. Distance(D, E) → distanceDE
  9. Segment(E, D) → e

AI Drawing Prompt Reference

Draw a line segment and mark a point on it. From the point, draw a perpendicular line. Take another point on the segment, connect the two points, and draw the perpendicular bisector of the segment. The perpendicular bisector intersects the perpendicular line at a point. Connect this point to the endpoints of the segment and to the foot of the perpendicular, labeling key points and segments to illustrate the geometric construction of a parabola.
The prompt above was compiled from the original drawing commands and is for reference only.