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Exploring Geometric Translations

Exploring Geometric Translations
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2019-11-26 23:29
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to perform geometric translations using GeoGebra. Core math concepts include vectors, distance calculation, and geometric transformations. Construction highlights: GeoGebra commands/objects used from the summary: Intersect, Dilate, Vector, Distance; objects: j, i, a, b, A, button1, c, d, B, text2, text1, button2, e, f, g, C, h, D, A', E, u, distanceEC, distanceAC, TextAC, C', v, F, G, distanceGD, TextGD, button3, k, button4. Suitable for middle school and above learning geometric transformations and vector applications.

GeoGebra Commands & Parameters

  1. Intersect(f, g) → C
  2. Intersect(f, h) → D
  3. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], C) → A'
  4. Vector(E, A') → u
  5. Distance(E, C) → distanceEC
  6. Distance(A, C) → distanceAC
  7. Dilate(C, If[1 < e ≤ 2, 2 - e, 0], D) → C'
  8. Vector(C, C') → v
  9. Intersect(g, xAxis) → F
  10. Intersect(f, g) → G
  11. Distance(G, D) → distanceGD

AI Drawing Prompt Reference

Draw a geometric transformation illustration showing vectors, distance calculation, and geometric transformations. Start by intersecting two lines at points C and D. Scale point A based on parameter e to get A', then draw vector u from E to A'. Calculate distances from E to C and A, and scale C to get C' via D. Finally, draw vector v from C to C' and the distance from G to D.
The prompt above was compiled from the original drawing commands and is for reference only.