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Animation 57: Line Transformation

Animation 57: Line Transformation
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2016-06-20 20:25
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the transformation process of a line, involving concepts of coordinate geometry and transformation. Using GeoGebra commands such as Segment, Midpoint, LineBisector, etc., it constructs midpoints, angle bisectors, and other geometric elements. Suitable for students at junior high school level and above to learn about line transformations and coordinate geometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Midpoint(f) → C_1
  3. LineBisector(f) → p
  4. Circle(C_1, (0.1 * f)) → c
  5. Intersect(c, f, 2) → D
  6. Intersect(c, p, 2) → E
  7. CircleSector(C_1, D, E) → d
  8. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C_1) → A'
  9. Segment(A, A') → h
  10. Dilate(C_1, If[1 < a ≤ 2, 2 - a, 0], B) → C'
  11. Segment(C_1, C') → i
  12. Rotate(A, If[2 < a ≤ 3, ((-(a - 2)) * π), (-π)], C_1) → A'_1
  13. Rotate(A', If[2 < a ≤ 3, ((a - 2) * π), π], C_1) → A''
  14. Segment(A'_1, A'') → h'
  15. Rotate(d, If[3 < a ≤ 4, ((a - 3) * π / 2), π / 2], C_1) → d'
  16. Point(p) → C
  17. Dilate(A, If[4 < a ≤ 5, 5 - a, 0], C) → A'_2
  18. Segment(A, A'_2) → g
  19. Dilate(B, If[5 < a ≤ 6, 6 - a, 0], C) → B'
  20. Segment(B, B') → j
  21. Angle(A, C, B) → α
  22. Rotate(A, If[6 < a ≤ 7, ((a - 6) * α), α], C) → A'_3
  23. Rotate(A'_2, If[6 < a ≤ 7, ((a - 6) * α), α], C) → G
  24. Segment(A'_3, G) → g'

AI Drawing Prompt Reference

Draw a line segment AB, find its midpoint C1, and then draw the angle bisector p of this segment. With C1 as the center and 10% of the length of AB as the radius, draw a circle c that intersects the line segment AB and the angle bisector p at points D and E, respectively, and use D and E to draw a sector d. Based on the parameter a, perform a series of transformations such as scaling, rotating, and translating to obtain a set of new line segments and shapes, including A', C', A'', A'_1, A'', A'_2, B', G, and A'_3, which demonstrate the transformation process of line segment AB and its related elements under different parameter values.
The prompt above was compiled from the original drawing commands and is for reference only.