等距变换案例三：平移、旋转与镜像的组合

GeoGebra 命令及参数

1. Point(Circle[A, 1.2851459061133876]) → B
2. Polygon(A, B, C, D, E, F) → preimage, a, b, c, d, e, f
3. Vector(G, H) → Vector
4. Line(I, J) → lineOfReflection
5. Translate(A, Vector) → A'
6. Translate(B, Vector) → B'
7. Translate(C, Vector) → C'
8. Translate(D, Vector) → D'
9. Translate(E, Vector) → E'
10. Translate(F, Vector) → F'
11. Polygon(A', B', C', D', E', F') → translated, a', b', c', d', e', f'
12. Mirror(A, lineOfReflection) → A'_{1}
13. Mirror(B, lineOfReflection) → B'_{1}
14. Mirror(C, lineOfReflection) → C'_{1}
15. Mirror(D, lineOfReflection) → D'_{1}
16. Mirror(E, lineOfReflection) → E'_{1}
17. Mirror(F, lineOfReflection) → F'_{1}
18. Polygon(A'_{1}, B'_{1}, C'_{1}, D'_{1}, E'_{1}, F'_{1}) → reflected, a'_{1}, b'_{1}, c'_{1}, d'_{1}, e'_{1}, f'_{1}
19. Rotate(A, α, Center) → A'_{2}
20. Rotate(B, α, Center) → B'_{2}
21. Rotate(C, α, Center) → C'_{2}
22. Rotate(D, α, Center) → D'_{2}
23. Rotate(E, α, Center) → E'_{2}
24. Rotate(F, α, Center) → F'_{2}
25. Polygon(A'_{2}, B'_{2}, C'_{2}, D'_{2}, E'_{2}, F'_{2}) → rotated, a'_{2}, b'_{2}, c'_{2}, d'_{2}, e'_{2}, f'_{2}
26. Line(K, lineOfReflection) → h
27. Point(h) → L
28. Vector(K, L) → Vector2
29. Mirror(A, lineOfReflection) → A'_{3}
30. Mirror(B, lineOfReflection) → B'_{3}
31. Mirror(C, lineOfReflection) → C'_{3}
32. Mirror(D, lineOfReflection) → D'_{3}
33. Mirror(E, lineOfReflection) → E'_{3}
34. Mirror(F, lineOfReflection) → F'_{3}
35. Polygon(A'_{3}, B'_{3}, C'_{3}, D'_{3}, E'_{3}, F'_{3}) → intermediary, a'_{3}, b'_{3}, c'_{3}, d'_{3}, e'_{3}, f'_{3}
36. Translate(A'_{3}, Vector2) → M
37. Translate(B'_{3}, Vector2) → N
38. Translate(C'_{3}, Vector2) → O
39. Translate(D'_{3}, Vector2) → P
40. Translate(E'_{3}, Vector2) → Q
41. Translate(F'_{3}, Vector2) → R
42. Polygon(M, N, O, P, Q, R) → image_{1}, m, n, o, p, q, r
43. Point(Circle[A_{3}, 1.2851459061133876]) → B_{1}
44. Polygon(A_{3}, B_{1}, C_{1}, D_{1}, E_{1}, F_{1}) → directImage, a_{1}, b_{1}, c_{1}, d_{1}, e_{1}, f_{1}
45. Point(Circle[U, 1.2935928228236204]) → B_2
46. Polygon(U, B_2, W, Z, G_1, H_1) → poly1, u, v, w, z_1, g_1, h_1