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Finding the Center of Rotation by Tim Brister

Finding the Center of Rotation by Tim Brister
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2013-12-15 07:34
PolygonAngleTransformationGeometric Construction
In collections Transformations and Symmetry Transformations and Symmetry
① This example demonstrates how to locate the center of rotation when given a rotated figure, using geometric construction tools. ② The core mathematical concept is rotation transformation in plane geometry, focusing on the property that the rotation center is equidistant from any pair of corresponding points, hence it lies on the perpendicular bisector of the segment joining them. ③ Construction details: from the summary, commands such as Polygon, Segment, Angle, and Rotate are used, creating original polygon poly1 and its rotated image poly1', along with segments connecting corresponding points (e.g., A and A'), their perpendicular bisectors, and intersections to determine the rotation center (points like K or L). ④ Suitable for upper middle school or high school geometry classes, this activity reinforces understanding of inverse rotation problems and develops geometric construction and logical reasoning skills.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E, F, G, H, I, J) → poly1, a, j, b, c, d, e, f, g, h, i
  2. Segment(K, L) → k
  3. Segment(L, M) → l
  4. Angle(M, L, K) → α
  5. Rotate(A, α, N) → A'
  6. Rotate(B, α, N) → B'
  7. Rotate(C, α, N) → C'
  8. Rotate(D, α, N) → D'
  9. Rotate(E, α, N) → E'
  10. Rotate(F, α, N) → F'
  11. Rotate(G, α, N) → G'
  12. Rotate(H, α, N) → H'
  13. Rotate(I, α, N) → I'
  14. Rotate(J, α, N) → J'
  15. Polygon(A', B', C', D', E', F', G', H', I', J') → poly1', a', j', b', c', d', e', f', g', h', i'

AI Drawing Prompt Reference

Draw an original polygon and its rotated image, then use geometric construction tools to find the center of rotation. First, draw polygon ABCDEFGHIJ, then rotate this polygon around a central point to get polygon A'B'C'D'E'F'G'H'I'J'. Next, connect corresponding vertices of the original and rotated polygons, such as A and A', and find the perpendicular bisector of the segment joining them. The intersection of these perpendicular bisectors is the center of rotation. Finally, draw all perpendicular bisectors and mark the center of rotation.
The prompt above was compiled from the original drawing commands and is for reference only.