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Locus of a Point Equidistant from Two Straight Lines

Locus of a Point Equidistant from Two Straight Lines
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2017-05-11 16:22
Coordinate GeometryGeometric ConstructionLocus
This example demonstrates the locus of a point equidistant from two straight lines. Key mathematical concepts include the concept of locus in coordinate geometry. Using GeoGebra commands such as OrthogonalLine (perpendicular line), Intersect (intersection), Point (point), etc., the locus of equidistant points can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry.

GeoGebra Commands & Parameters

  1. Textfield() → InputBox1
  2. Textfield(f) → InputBox2
  3. Textfield(g) → InputBox3
  4. OrthogonalLine(P, g) → h
  5. OrthogonalLine(P, f) → i
  6. Intersect(f, i) → P''
  7. Segment(P, P'') → j
  8. Point(f) → A
  9. Point(f) → B
  10. Angle(P, P'', A) → α
  11. OrthogonalLine(P, g) → l
  12. Intersect(g, l) → P'
  13. Segment(P, P') → k

AI Drawing Prompt Reference

Draw two lines f and g, and find the locus of points equidistant from f and g. First, take two points A and B on f, then draw perpendicular lines from A and B to g, and find their intersections with g, which are P' and P''. Then, draw line segment P'P''. Next, find the symmetric points of P' and P'' with respect to f, which are P and P''. Finally, draw line segment P and P''.
The prompt above was compiled from the original drawing commands and is for reference only.