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Perpendicular from a point to a line segment

Perpendicular from a point to a line segment
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2017-12-15 02:57
Coordinate GeometryOptimizationGeometric Construction
In collections Constructions Project
This example demonstrates constructing a perpendicular line from a point outside a segment to the segment itself, exploring the concept of the shortest distance. Core math concepts include perpendicular lines, the shortest distance theorem, and coordinate geometry. It uses commands like Segment, Point, Circle, Intersect, and Line in GeoGebra for construction. Suitable for high school coordinate geometry lessons or math clubs.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Point(f) → C
  3. Circle(C, 2.1005813719000814) → c
  4. Intersect(c, f, 2) → D
  5. Intersect(c, f, 1) → E
  6. Circle(E, D) → d
  7. Circle(D, E) → e
  8. Intersect(d, e, 1) → F
  9. Line(C, F) → g

AI Drawing Prompt Reference

Draw a line segment and a circle centered at a point outside the segment. Let the circle intersect the segment at two points. Then, draw circles centered at these two intersection points and find their intersection point. Connect this point to the original point outside the segment to form a perpendicular line, demonstrating the shortest distance from a point to a line segment.
The prompt above was compiled from the original drawing commands and is for reference only.