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270 Degree Counterclockwise Rotation

270 Degree Counterclockwise Rotation
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2017-04-05 22:25
AngleVectorCoordinate GeometryTransformationGeometric Construction
In collections Rotations
This example demonstrates the process and result of rotating a point or figure 270 degrees counterclockwise around the origin. Key math concepts include rotation, angles, coordinate transformation, and vectors. It utilizes commands and objects like Textfield, Segment, Midpoint, Rotate, CircleArc, Point, and Vector as outlined in the construction summary. Suitable for high school students learning analytical geometry and geometric transformations, or for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Textfield(A) → InputBox1
  2. Segment(O, A) → f
  3. Midpoint(f) → B
  4. Rotate(A, 270°, O) → A'
  5. Segment(O, A') → g
  6. Midpoint(g) → C
  7. CircleArc(O, B, C) → c
  8. Point(c) → D
  9. Vector(D, C) → u

AI Drawing Prompt Reference

Draw a point A, then draw a segment f from the origin O to A. Find the midpoint B of segment f. Rotate point A 270 degrees counterclockwise to get A', then draw a segment g from O to A'. Find the midpoint C of segment g. Draw a circular arc c from O with B and C as endpoints. Pick a point D on arc c, then draw a vector u from D to C.
The prompt above was compiled from the original drawing commands and is for reference only.