MathPlotAI Logo MathPlotAI

Perpendicular Fitting

Perpendicular Fitting
Loading the math board and drawing, please wait…
2019-02-26 17:12
FunctionCoordinate GeometryOptimization
This example demonstrates the concept of perpendicular fitting. It involves key mathematical concepts such as lines, perpendicular lines, intersections, segments, and fitting lines. Using GeoGebra commands like Line, OrthogonalLine, Intersect, Segment, and FitLineY, the construction of perpendicular fitting is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(C, a) → b
  3. OrthogonalLine(D, a) → c
  4. OrthogonalLine(E, a) → d
  5. OrthogonalLine(F, a) → e
  6. OrthogonalLine(G, a) → f
  7. OrthogonalLine(H, a) → g
  8. OrthogonalLine(I, a) → h
  9. Intersect(a, b) → J
  10. Intersect(a, c) → K
  11. Intersect(a, d) → L
  12. Intersect(a, e) → M
  13. Intersect(a, f) → N
  14. Intersect(a, g) → O
  15. Intersect(a, h) → P
  16. Segment(C, J) → i
  17. Segment(D, K) → j
  18. Segment(L, E) → k
  19. Segment(F, M) → l
  20. Segment(G, N) → m
  21. Segment(H, O) → n
  22. Segment(P, I) → p
  23. Sum(L_2) → sum
  24. FitLineY(L_3) → q
  25. Line(Q, R) → r
  26. OrthogonalLine(C, xAxis) → s
  27. OrthogonalLine(E, xAxis) → t
  28. OrthogonalLine(D, xAxis) → a_1
  29. OrthogonalLine(F, xAxis) → b_1
  30. OrthogonalLine(G, xAxis) → c_1
  31. OrthogonalLine(H, xAxis) → d_1
  32. OrthogonalLine(I, xAxis) → e_1
  33. Intersect(r, s) → S
  34. Intersect(r, t) → T
  35. Intersect(r, a_1) → U
  36. Intersect(r, b_1) → V
  37. Intersect(r, c_1) → W
  38. Intersect(r, d_1) → Z
  39. Intersect(r, e_1) → A_1
  40. Segment(C, S) → f_1
  41. Segment(E, T) → g_1
  42. Segment(D, U) → h_1
  43. Segment(F, V) → i_1
  44. Segment(G, W) → j_1
  45. Segment(H, Z) → k_1
  46. Segment(I, A_1) → l_1
  47. Sum(L_5) → sum_2

AI Drawing Prompt Reference

Draw a line a on the coordinate system and find several lines b to h that are perpendicular to it. Then, find the intersections of these perpendicular lines with line a, labeled J to P. Connect points C, D, E, F, G, H, and I to these intersections to form several segments i to p. Next, find the sum of these segments as sum, and fit a best-fit line q. Finally, draw several lines perpendicular to the x-axis, labeled s to e_1, and find their intersections with the fitted line q, labeled S to A_1. Connect points C, E, D, F, G, H, and I to these intersections to form several segments f_1 to l_1, and find the sum of these segments as sum_2.
The prompt above was compiled from the original drawing commands and is for reference only.