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Locus of Points Equidistant from Two Parallel Lines

Locus of Points Equidistant from Two Parallel Lines
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2017-12-18 14:02
VectorGeometric ConstructionLocus
In collections Locus
This example demonstrates the locus of points equidistant from two parallel lines. Key mathematical concepts include geometric construction and locus. Using GeoGebra commands such as OrthogonalLine, Intersect, Segment, etc., the construction of points equidistant from two parallel lines is illustrated. Suitable for high school geometry students or anyone interested in geometric loci.

GeoGebra Commands & Parameters

  1. OrthogonalLine(P, L_2) → f
  2. Intersect(L_2, f) → C
  3. Intersect(f, L_1) → D
  4. Segment(P, C) → g
  5. Segment(P, D) → h
  6. Point(L_2) → A
  7. Point(L_1) → E
  8. Angle(A, C, P) → α
  9. Angle(P, D, E) → γ
  10. If(abs(g - h) ≤ 0.02, P) → B

AI Drawing Prompt Reference

Draw two parallel lines L1 and L2, then choose a point P on L2 and construct the perpendicular line f from P to L2. Find the intersection points D of f and L1, and C of f and L2. Draw line segments g from P to C and h from P to D. Finally, locate point B such that the difference in lengths of g and h is less than 0.02.
The prompt above was compiled from the original drawing commands and is for reference only.