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Coplanar Equidistant Points (Part 1) - Quick

Coplanar Equidistant Points (Part 1) - Quick
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2017-01-19 22:27
CircleCoordinate GeometryGeometric ConstructionSlider AnimationLocus
① This interactive GeoGebra example quickly demonstrates the set of coplanar points that are equidistant from the endpoints of a segment, which is exactly the perpendicular bisector of that segment. ② Core math concepts include midpoint, perpendicular bisector, equidistant points, circle intersections, and geometric locus. ③ Construction uses commands: Segment to define AB, LineBisector for the perpendicular bisector, Point for a movable point C on the segment, Circle centered at C with radius CA, Intersect to find points where the circle meets the bisector, Midpoint, Distance, and Angle tools, plus a button and text for interactivity. ④ Suitable for middle school to high school students learning the properties of perpendicular bisectors, and for teachers demonstrating geometric constructions dynamically.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. LineBisector(a) → p
  3. Point(p) → C
  4. Circle(A, C) → c
  5. Segment(A, C) → d
  6. Intersect(p, a) → D
  7. Segment(A, C) → e
  8. Segment(C, B) → f
  9. Midpoint(a) → M
  10. Segment(A, M) → i
  11. Segment(M, B) → j
  12. Distance(A, C) → k
  13. Distance(C, B) → l
  14. LineBisector(a) → g
  15. Midpoint(a) → E
  16. Angle(B, E, C) → α

AI Drawing Prompt Reference

Draw a line segment AB, find its midpoint, and draw the perpendicular bisector. Place a movable point C on the segment, draw a circle centered at C with radius AC, and find the intersection points of the circle with the bisector, which are equidistant from A and B. Show segments AC and BC, and label the midpoint, lengths of AC and BC, and the angle at point E between segments BE and CE.
The prompt above was compiled from the original drawing commands and is for reference only.