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Midpoint Perpendicular

Midpoint Perpendicular
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2016-01-18 20:43
VectorCoordinate GeometryGeometric Construction
This example illustrates the concept of midpoint perpendicular. Key mathematical concepts include straight lines, perpendicular lines, and midpoints. Using GeoGebra commands such as LineBisector, OrthogonalLine, and Midpoint, the construction of midpoint perpendicular is demonstrated. Suitable for students at the junior high school level and above to learn basic concepts in coordinate geometry.

GeoGebra Commands & Parameters

  1. Line(B, A) → a
  2. LineBisector(B, A) → b
  3. OrthogonalLine(B, a) → c
  4. Intersect(a, b) → C
  5. Midpoint(C, A) → C'
  6. Circle(B, C') → d
  7. Intersect(d, b, 2) → D
  8. Circle(A, D) → e
  9. Intersect(d, e, 2) → E
  10. OrthogonalLine(B, a) → f
  11. OrthogonalLine(A, a) → g
  12. Intersect(e, g, 2) → F
  13. Intersect(d, f, 1) → G
  14. Rotate(F, Min[Max[(t * 180), 0], 180]°, A) → F'
  15. Rotate(G, Min[Max[((t - 1) * 180), 0], 180]°, B) → G'
  16. CircleArc(A, F, F') → h
  17. CircleArc(B, G, G') → k
  18. Ellipse(E, D, F) → p
  19. Intersect(p, b, 2) → H
  20. Intersect(p, b, 1) → I
  21. Translate(I, ((H - I) * Min[Max[t - 2, 0], 1])) → I'
  22. Segment(I, I') → i
  23. Vector(J, K) → u

AI Drawing Prompt Reference

Draw a geometric figure consisting of lines, perpendicular lines, circles, and an ellipse. First, draw two lines. Then, construct perpendicular lines to these lines. Next, find the intersection point of the lines and draw a perpendicular from the midpoint to one of the lines. Then, draw a circle centered at the intersection point. Finally, intersect the circle with the perpendicular lines to obtain points, and use these points to construct an ellipse. This figure illustrates the relationships between lines, perpendiculars, circles, and ellipses, suitable for learning coordinate geometry.
The prompt above was compiled from the original drawing commands and is for reference only.