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2.4 Rotation: Geometric Transformation and Graph Construction

2.4 Rotation: Geometric Transformation and Graph Construction
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2023-03-22 20:24
TriangleCircleVectorTransformation
In collections geometriadinamica.es
This example demonstrates the application of rotation transformation in geometric figures. The key mathematical concepts involved include rotation, vectors, circles, and triangles. Construction points include using GeoGebra commands such as Line, Point, Vector, Rotate, Angle, etc. Suitable for middle or high school mathematics learning to understand geometric transformations and properties.

GeoGebra Commands & Parameters

  1. Line(D, C) → g
  2. Point(g) → D_1
  3. Vector(N_8, O_8) → u
  4. Vector(N_8, A_{18}) → w
  5. Min(180, (a * 180)) → rr
  6. OrthogonalLine(F, g) → b
  7. Point(b) → O
  8. Circle(F, O) → d
  9. Rotate(O, rr°, F) → O'
  10. Angle(O, F, O') → α
  11. CircleSector(F, O, O') → e
  12. Rotate(pic2, rr°, E) → pic2'

AI Drawing Prompt Reference

Create a plane diagram with a baseline line and points that establish a reference direction and vector. Choose a circle using a specified center point and a point on the reference line to define the radius. Determine a rotation angle based on a scaled scalar value (a mapping that yields a value between 0 and 180 degrees). Rotate the key reference point around the circle’s center by this angle to obtain a new point, and measure the angle at the center between the original and rotated positions. Finally, draw the circular sector on the circle bounded by the two corresponding radius directions.
The prompt above was compiled from the original drawing commands and is for reference only.