MathPlotAI Logo MathPlotAI

Perpendicular Line through a Point on a Given Line

Perpendicular Line through a Point on a Given Line
Loading the math board and drawing, please wait…
2015-03-27 18:13
AngleCoordinate GeometryGeometric Construction
In collections Compass constructions
This example demonstrates how to construct a perpendicular line through a point on a given line. It involves core mathematical concepts such as perpendicularity, distance from a point to a line, and geometric construction. The construction uses commands/objects like Line, Point, Circle, Mirror, Intersect, Rotate, CircumcircleArc, Segment, Polygon, and Angle in GeoGebra. Suitable for high school mathematics or coordinate geometry instruction.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Point(a) → C
  3. Point(a) → E
  4. Circle(E, I) → d
  5. Mirror(d, C) → d'
  6. Circle(C, E) → c
  7. Intersect(c, a, 2) → G
  8. Intersect(d, d', 2) → H
  9. Intersect(d, d') → F, J, ,
  10. Line(H, F) → b
  11. Rotate(E, α, C) → E'
  12. Rotate(E, (-α), C) → E'_1
  13. Rotate(G, α, C) → G'
  14. Rotate(G, (-α), C) → G'_1
  15. Rotate(F, α, E) → F'
  16. Rotate(F, (-α), E) → F'_1
  17. Rotate(F, α, G) → F'_2
  18. Rotate(F, (-α), G) → F'_3
  19. Rotate(H, α, E) → H'
  20. Rotate(H, (-α), E) → H'_1
  21. Rotate(H, α, G) → H'_2
  22. Rotate(H, (-α), G) → H'_3
  23. CircumcircleArc(E', E, E'_1) → e
  24. CircumcircleArc(G'_1, G, G') → f
  25. CircumcircleArc(F', F, F'_1) → g
  26. CircumcircleArc(F'_2, F, F'_3) → h
  27. CircumcircleArc(H', H, H'_1) → k
  28. CircumcircleArc(H'_3, H, H'_2) → p
  29. Segment(C, G') → i
  30. Segment(C, G) → j
  31. Segment(C, G) → l
  32. Segment(C, G'_1) → m
  33. Segment(C, E'_1) → n
  34. Segment(E, C) → q
  35. Segment(E', C) → r
  36. Segment(F', E) → s
  37. Segment(F, E) → t
  38. Segment(F'_1, E) → b_1
  39. Segment(F'_2, G) → c_1
  40. Segment(F, G) → d_1
  41. Segment(F'_3, G) → e_1
  42. Segment(E, H'_1) → f_1
  43. Segment(H, E) → g_1
  44. Segment(H', E) → h_1
  45. Segment(H'_3, G) → i_1
  46. Segment(H, G) → j_1
  47. Segment(H'_2, G) → k_1
  48. Polygon(E, H, G, F) → poly1, e_2, h_2, g_2, f_2
  49. Angle(F, C, E) → β

AI Drawing Prompt Reference

Construct a perpendicular line through a point on a given line. Start by drawing a line AB with points A and B. Then, take point C on the line and draw a circle with center C. Draw another circle with center E, and find the intersection points G and H. Use reflections and rotations to find the symmetric points of F and H, and draw the perpendicular line b. Finally, construct arcs and segments to form a quadrilateral.
The prompt above was compiled from the original drawing commands and is for reference only.