MathPlotAI Logo MathPlotAI

Perpendicular Lines in the Coordinate Plane: Quick Exploration

Perpendicular Lines in the Coordinate Plane: Quick Exploration
Loading the math board and drawing, please wait…
2018-03-03 00:08
VectorCoordinate GeometryGeometric Construction
This example demonstrates the properties of perpendicular lines in the coordinate plane, involving key mathematical concepts such as straight lines and slope. Using GeoGebra commands like Line, Slope, and OrthogonalLine, students can quickly explore and discover these properties. Suitable for middle school and above students for geometric construction and exploration.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Slope(f) → a
  3. Denominator(a) → run
  4. Numerator(a) → rise
  5. OrthogonalLine(C, f) → g
  6. Intersect(f, g) → D
  7. Angle(B, D, C) → α
  8. Intersect(h, i) → E
  9. Polygon(A, E, B) → t1, b, a_1, e
  10. Segment(A, E) → j
  11. Segment(E, B) → k
  12. Segment(B, A) → l
  13. Distance(C, F) → distanceCF
  14. Distance(B, E) → distanceBE
  15. Intersect(g, n) → G
  16. Dilate(A, If[0 < c ≤ 1, 1 - c, 0], G) → A'
  17. Vector(A, A') → u
  18. Translate(A, u) → A'_1
  19. Translate(E, u) → E'
  20. Translate(B, u) → B'
  21. Polygon(A'_1, E', B') → t1', b', a'_1, e'
  22. Segment(A'_1, E') → p
  23. Segment(E', B') → q
  24. Segment(B', A'_1) → r
  25. Angle(B', E', A'_1) → β
  26. Angle(B, E, A) → γ
  27. Rotate(A'_1, If[1 < c ≤ 2, ((c - 1) * π / 2), π / 2], G) → H
  28. Rotate(E', If[1 < c ≤ 2, ((c - 1) * π / 2), π / 2], G) → E''
  29. Rotate(B', If[1 < c ≤ 2, ((c - 1) * π / 2), π / 2], G) → B''
  30. Polygon(H, E'', B'') → t1'', b'', h_1, e''
  31. Segment(G, E'') → s
  32. Segment(E'', B'') → t
  33. Segment(B'', G) → d
  34. Angle(B'', E'', G) → δ