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Perpendicular Through a Point on a Line

Perpendicular Through a Point on a Line
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2016-11-09 01:02
TriangleCircleCoordinate Geometry
In collections Construction
This example demonstrates how to construct a perpendicular line through a point on a given line. Key mathematical concepts include the properties of lines, points, and perpendicular lines. GeoGebra commands used include Line, Point, Intersect, and Segment. Suitable for students at the middle school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Point(f) → C
  3. Point(f) → D
  4. Circle(C, D) → c
  5. Intersect(c, f, 2) → E
  6. Segment(E, C) → g
  7. Circle(E, g + 0.5) → d
  8. Circle(D, g + 0.5) → e
  9. Intersect(d, e) → F, G, ,
  10. Line(G, F) → h
  11. Segment(E, F) → i
  12. Segment(F, D) → j

AI Drawing Prompt Reference

Draw a line f, then select two points C and D on the line to form a circle c with these points as the diameter. Circle c intersects line f at point E. Connect point E and point C to form segment g. Draw two circles d and e with point E and point C as centers and radius g+0.5. Circles d and e intersect at points F and G. Connect point F and E to form line h, and connect point F and D to form segment j.
The prompt above was compiled from the original drawing commands and is for reference only.