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Investigation of Rotations with Coordinates by David Lurie

Investigation of Rotations with Coordinates by David Lurie
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2016-12-07 21:38
TrigonometryCoordinate Geometry
This example demonstrates how to perform rotations using coordinates. Key mathematical concepts include rotation, trigonometric functions, and coordinate geometry. Using commands like Polygon, Intersect, Rotate, Segment, and Angle, the construction of rotated figures is illustrated. Suitable for students in middle school and above to learn about rotation transformations and trigonometric functions.

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 the origin O to get a new triangle A'B'C'. First, draw the intersection point O of the x-axis and y-axis as the rotation center. Then, draw triangle ABC, and rotate points A, B, and C to get A', B', and C' respectively. Finally, draw the new triangle A'B'C'. Pay attention to the changes in angles before and after the rotation.
The prompt above was compiled from the original drawing commands and is for reference only.