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Investigation of Rotations with Coordinates

Investigation of Rotations with Coordinates
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2016-12-07 21:24
Coordinate GeometryTransformationGeometric Construction
This example demonstrates how to perform rotations using coordinates. Key mathematical concepts include rotation, coordinate geometry, and vectors. Using commands like Polygon, Intersect, Rotate, Segment, and Angle in GeoGebra, you can construct the rotated figures. Suitable for students in middle school and above learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a_1, b
  2. Intersect(xAxis, yAxis) → O
  3. Rotate(A, a, O) → A'
  4. Rotate(B, a, O) → B'
  5. Rotate(C, a, O) → C'
  6. Polygon(A', B', C') → poly1', c', a', b'
  7. Segment(A, O) → d
  8. Segment(O, A') → e
  9. Angle(A, O, A') → α

AI Drawing Prompt Reference

Draw a triangle ABC, then rotate it 90 degrees around point O to get triangle A'B'C'. First, find the intersection point O of the x-axis and y-axis. Then, connect points A, B, and C to form triangle ABC. Next, rotate triangle ABC 90 degrees counterclockwise around point O to get A'B'C'. Finally, draw line segments AO and A'O, and measure the angle ∠AOA'.
The prompt above was compiled from the original drawing commands and is for reference only.