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Reflections on a Grid

Reflections on a Grid
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2014-06-13 05:17
Coordinate GeometryGeometric Construction
This example demonstrates reflecting objects on a Cartesian grid using horizontal, vertical, and diagonal mirror lines. Hide/Show the equations to choose the mirror line displacement. It involves core math concepts like reflection symmetry, coordinate transformation, and geometric transformation. Constructed using GeoGebra commands like Polygon and Mirror, it visually tracks the reflection process and object movement. Suitable for middle school and above, helping students understand spatial transformations and geometric constructions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E, F, G, H) → poly1, a, b, c, d, e, f, g, h
  2. Mirror(A, j) → A'
  3. Mirror(B, j) → B'
  4. Mirror(C, j) → C'
  5. Mirror(D, j) → D'
  6. Mirror(E, j) → E'
  7. Mirror(F, j) → F'
  8. Mirror(G, j) → G'
  9. Mirror(H, j) → H'
  10. Polygon(A', B', C', D', E', F', G', H') → poly1', a', b', c', d', e', f', g', h'
  11. Mirror(A, y = l) → A'_1
  12. Mirror(B, y = l) → B'_1
  13. Mirror(C, y = l) → C'_1
  14. Mirror(D, y = l) → D'_1
  15. Mirror(E, y = l) → E'_1
  16. Mirror(F, y = l) → F'_1
  17. Mirror(G, y = l) → G'_1
  18. Mirror(H, y = l) → H'_1
  19. Polygon(A'_1, B'_1, C'_1, D'_1, E'_1, F'_1, G'_1, H'_1) → poly1'_1, a'_1, b'_1, c'_1, d'_1, e'_1, f'_1, g'_1, h'_1
  20. Mirror(A, p) → A'_2
  21. Mirror(B, p) → B'_2
  22. Mirror(C, p) → C'_2
  23. Mirror(D, p) → D'_2
  24. Mirror(E, p) → E'_2
  25. Mirror(F, p) → F'_2
  26. Mirror(G, p) → G'_2
  27. Mirror(H, p) → H'_2
  28. Polygon(A'_2, B'_2, C'_2, D'_2, E'_2, F'_2, G'_2, H'_2) → poly1'_2, a'_2, b'_2, c'_2, d'_2, e'_2, f'_2, g'_2, h'_2

AI Drawing Prompt Reference

In a Cartesian coordinate system, draw an eight-sided polygon first. Then reflect this polygon successively across a horizontal line, a vertical line, and two diagonal lines, creating new polygons for each reflection to show the reflection process and object movement. Toggle the visibility of equations to choose different mirror lines, visually demonstrating reflection symmetry, coordinate transformation, and geometric transformation concepts.
The prompt above was compiled from the original drawing commands and is for reference only.