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Day 6 - Dilation

Day 6 - Dilation
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2017-03-14 06:16
VectorSolid GeometryGeometric Construction
This example demonstrates dilation in three-dimensional space. Key math concepts include dilation, 3D vectors, solids or 3D shapes, and median lines. Construction highlights the use of GeoGebra commands like Segment and Dilate, involving objects such as points A, B, C, D, A', B', C', D'. Suitable for high school and above students to explore the properties and applications of 3D geometric transformations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, D) → h
  4. Segment(D, A) → i
  5. Dilate(A, r, X) → A'
  6. Dilate(B, r, X) → B'
  7. Segment(A', B') → f'
  8. Dilate(B, r, X) → B'_1
  9. Dilate(C, r, X) → C'
  10. Segment(B'_1, C') → g'
  11. Dilate(C, r, X) → C'_1
  12. Dilate(D, r, X) → D'
  13. Segment(C'_1, D') → h'
  14. Dilate(D, r, X) → D'_1
  15. Dilate(A, r, X) → A'_1
  16. Segment(D'_1, A'_1) → i'

AI Drawing Prompt Reference

Draw a 3D illustration showing dilation transformation, featuring a quadrilateral and its scaled version. Start by drawing the four sides of the original quadrilateral. Then scale each vertex of the quadrilateral from a center point by a certain ratio to get the scaled vertices. Next, connect these scaled vertices to form the scaled quadrilateral and also connect the midpoints of the corresponding sides to highlight the properties of the dilation.
The prompt above was compiled from the original drawing commands and is for reference only.