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Facial Line-Symmetry: Mirror Transformations and Geometric Construction

Facial Line-Symmetry: Mirror Transformations and Geometric Construction
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2018-12-09 19:19
FunctionCoordinate GeometrySolid GeometryTransformationGeometric Construction
① This GeoGebra example demonstrates line symmetry (axial symmetry) on a facial-like figure, showing how mirror transformation maps the original shape across an axis and verifies equal distances from corresponding points to the axis. ② Core mathematical concepts include axial symmetry, mirror transformation, distance measurement, and coordinate relationships of symmetric points, with extensions to quadratic functions, pyramids (solid geometry), and probability. ③ Construction highlights: using Segment, Mirror, and Distance commands, objects A, B, f, C, g, D, h, i, E, F, j are created, along with text1-4 displaying distances such as distanceOK', distancePL', distanceQH', distanceRG' to confirm that symmetric points (K', H', N', M', G', L') are equidistant from the symmetry axis. ④ Suitable for middle and high school students learning geometric transformations, symmetry properties, and coordinate geometry, as well as for teachers demonstrating symmetry visually and dynamically in class.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, D) → h
  4. Segment(D, A) → i
  5. Segment(E, F) → j
  6. Mirror(K, j) → K'
  7. Mirror(H, j) → H'
  8. Mirror(N, j) → N'
  9. Mirror(M, j) → M'
  10. Mirror(G, j) → G'
  11. Mirror(L, j) → L'
  12. Distance(O, K') → distanceOK'
  13. Distance(P, L') → distancePL'
  14. Distance(Q, H') → distanceQH'
  15. Distance(R, G') → distanceRG'
  16. Distance(S, N') → distanceSN'
  17. Distance(T, M') → distanceTM'
  18. Segment(K', O) → k
  19. Segment(L', P) → l
  20. Segment(G', R) → m
  21. Segment(H', Q) → n
  22. Segment(N', S) → p
  23. Segment(M', T) → q
  24. Distance(K', O) → distanceK'O

AI Drawing Prompt Reference

Draw a face-like closed shape formed by four connected line segments, and a separate line segment as the axis of symmetry. Reflect six key points of the face across this axis to get six mirrored points. Then connect each mirrored point to its corresponding original point on the other side, and measure the distances of these connecting segments as well as the distances from the mirrored points to their counterparts. Display these distance values as text labels to verify that symmetric points are equidistant from the axis. This illustrates axial symmetry and mirror transformation.
The prompt above was compiled from the original drawing commands and is for reference only.