Geometric Transformations and Function Graphs in Geogebra

GeoGebra Commands & Parameters

1. Midpoint(N_1, O_1) → V_1
2. Midpoint(L_1, M_1) → S_1
3. Circle(A, P_0) → c
4. Rotate(P_0, α, A) → A_1
5. If(a < 1, a, 1) → d
6. Rotate(A_1, ((-d) * α / 2), P_0) → P_1
7. Rotate(A, ((-d) * α / 2), P_0) → E_1
8. Rotate(P_1, α, E_1) → A_2
9. Rotate(A_2, ((-d) * α), P_1) → P_2
10. Rotate(E_1, ((-d) * α), P_1) → E_2
11. Rotate(P_2, α, E_2) → A_3
12. Rotate(A_3, ((-d) * α), P_2) → P_3
13. Rotate(E_2, ((-d) * α), P_2) → E_3
14. Rotate(P_3, α, E_3) → A_4
15. Rotate(A_4, ((-d) * α), P_3) → P_4
16. Rotate(E_3, ((-d) * α), P_3) → E_4
17. Rotate(E_4, ((-d) * α), P_4) → E_5
18. Rotate(P_4, α, E_4) → A_5
19. Rotate(A_5, ((-d) * α), P_4) → P_5
20. Rotate(E_5, ((-d) * α), P_5) → E_6
21. Rotate(P_5, α, E_5) → A_6
22. Rotate(A_6, ((-d) * α), P_5) → P_6
23. Rotate(E_6, ((-d) * α), P_6) → E_7
24. Rotate(P_6, α, E_6) → A_7
25. Rotate(A_7, ((-d) * α), P_6) → P_7
26. Rotate(E_7, ((-d) * α), P_7) → E_8
27. Rotate(P_7, α, E_7) → A_8
28. Rotate(A_8, ((-d) * α), P_7) → P_8
29. Line(P_0, A) → b
30. Mirror(E_1, b) → B
31. Mirror(E_2, b) → C
32. Mirror(E_3, b) → D
33. Mirror(E_4, b) → E
34. Mirror(E_6, b) → F
35. Mirror(E_5, b) → G
36. Mirror(E_7, b) → H
37. Mirror(E_8, b) → I
38. Mirror(P_1, b) → Q
39. Mirror(P_2, b) → R
40. Mirror(P_3, b) → S
41. Mirror(P_4, b) → T
42. Mirror(P_5, b) → U
43. Mirror(P_6, b) → V
44. Mirror(P_7, b) → W
45. Mirror(P_8, b) → Y
46. Polygon(P_6, P_5, T, U, V, W, Y, I, W, H, V, F, P_4, U, G, T, E, S, D, R, C, Q, B, P_3, P_0, E_1, P_1, E_2, P_2, E_3, P_3, E_4, P_4, E_5, P_2, P_5, E_6, P_6, E_7, P_7, P_1, P_0, Q, R, S) → R_1, e, n, p, q, r, s, t, a_1, b_1, c_1, d_1, f, e_1, f_1, g_1, h_1, i_1, j_1, k_1, l_1, m_1, n_1, g, p_1, q_1, r_1, s_1, t_1, a_2, b_2, c_2, d_2, e_2, h, f_2, g_2, h_2, i_2, j_2, k_2, i, j, k, l, m
47. Midpoint(P_0, B) → K_1
48. Vector(S_1, T_1) → v
49. Vector(S_1, U_1) → u
50. Vector(V_1, W_1) → w
51. Vector(V_1, Y_1) → z
52. If(a < 1.2, 0, a - 1.2) → dd
53. Mirror(P_6, A) → P_6'
54. Mirror(P_5, A) → P_5'
55. Mirror(P_4, A) → P_4'
56. Mirror(P_3, A) → P_3'
57. Mirror(P_2, A) → P_2'
58. Mirror(P_1, A) → P_1'
59. Mirror(P_0, A) → P_0'
60. Mirror(Q, A) → Q'
61. Mirror(R, A) → R'
62. Mirror(S, A) → S'
63. Mirror(T, A) → T'
64. Mirror(U, A) → U'
65. Mirror(V, A) → V'
66. Mirror(W, A) → W'
67. Mirror(Y, A) → Y'
68. Mirror(I, A) → I'
69. Mirror(W, A) → W'_1
70. Mirror(H, A) → H'
71. Mirror(V, A) → V'_1
72. Mirror(F, A) → F'
73. Mirror(U, A) → U'_1
74. Mirror(G, A) → G'
75. Mirror(T, A) → T'_1
76. Mirror(E, A) → E'
77. Mirror(S, A) → S'_1
78. Mirror(D, A) → D'
79. Mirror(R, A) → R'_1
80. Mirror(C, A) → C'
81. Mirror(Q, A) → Q'_1
82. Mirror(B, A) → B'
83. Mirror(P_0, A) → P_9
84. Mirror(E_1, A) → E_1'
85. Mirror(P_1, A) → P_{10}
86. Mirror(E_2, A) → E_2'
87. Mirror(P_2, A) → P_{11}
88. Mirror(E_3, A) → E_3'
89. Mirror(P_3, A) → P_{12}
90. Mirror(E_4, A) → E_4'
91. Mirror(P_4, A) → P_{13}
92. Mirror(E_5, A) → E_5'
93. Mirror(P_5, A) → P_{14}
94. Mirror(E_6, A) → E_6'
95. Mirror(P_6, A) → P_{15}
96. Mirror(E_7, A) → E_7'
97. Mirror(P_7, A) → P_7'
98. Polygon(P_6', P_5', T', U', V', W', Y', I', W'_1, H', V'_1, F', P_4', U'_1, G', T'_1, E', S'_1, D', R'_1, C', Q'_1, B', P_3', P_9, E_1', P_{10}, E_2', P_{11}, E_3', P_{12}, E_4', P_{13}, E_5', P_2', P_{14}, E_6', P_{15}, E_7', P_7', P_1', P_0', Q', R', S') → R_1', p_6', s', t', u', v', w', y', i', w'_1, h', v'_1, p_5', f', u'_1, g', t'_1, e', s'_1, d', r'_1, c', q'_1, p_4', b', p_9, e_1', p_{10}, e_2', p_{11}, e_3', p_{12}, e_4', p_{13}, p_3', e_5', p_{14}, e_6', p_{15}, e_7', p_7', p_2', p_1', p_0', q', r'
99. Vector(W', H') → u_1
100. Translate(P_6', v_1) → P_6''
101. Translate(P_5', v_1) → P_5''
102. Translate(P_4', v_1) → P_4''
103. Translate(P_3', v_1) → P_3''
104. Translate(P_2', v_1) → P_2''
105. Translate(P_1', v_1) → P_1''
106. Translate(P_0', v_1) → P_0''
107. Translate(Q', v_1) → Q''
108. Translate(R', v_1) → R''
109. Translate(S', v_1) → S''
110. Translate(T', v_1) → T''
111. Translate(U', v_1) → U''
112. Translate(V', v_1) → V''
113. Translate(W', v_1) → W''
114. Translate(Y', v_1) → Y''
115. Translate(I', v_1) → I''
116. Translate(W'_1, v_1) → W'_1'
117. Translate(H', v_1) → H''
118. Translate(V'_1, v_1) → V'_1'
119. Translate(F', v_1) → F''
120. Translate(U'_1, v_1) → U'_1'
121. Translate(G', v_1) → G''
122. Translate(T'_1, v_1) → T'_1'
123. Translate(E', v_1) → E''
124. Translate(S'_1, v_1) → S'_1'
125. Translate(D', v_1) → D''
126. Translate(R'_1, v_1) → R'_1'
127. Translate(C', v_1) → C''
128. Translate(Q'_1, v_1) → Q'_1'
129. Translate(B', v_1) → B''
130. Translate(P_9, v_1) → P_9'
131. Translate(E_1', v_1) → E_1''
132. Translate(P_{10}, v_1) → P_{10}'
133. Translate(E_2', v_1) → E_2''
134. Translate(P_{11}, v_1) → P_{11}'
135. Translate(E_3', v_1) → E_3''
136. Translate(P_{12}, v_1) → P_{12}'
137. Translate(E_4', v_1) → E_4''
138. Translate(P_{13}, v_1) → P_{13}'
139. Translate(E_5', v_1) → E_5''
140. Translate(P_{14}, v_1) → P_{14}'
141. Translate(E_6', v_1) → E_6''
142. Translate(P_{15}, v_1) → P_{15}'
143. Translate(E_7', v_1) → E_7''
144. Translate(P_7', v_1) → P_7''
145. Polygon(P_6'', P_5'', T'', U'', V'', W'', Y'', I'', W'_1', H'', V'_1', F'', P_4'', U'_1', G'', T'_1', E'', S'_1', D'', R'_1', C'', Q'_1', B'', P_3'', P_9', E_1'', P_{10}', E_2'', P_{11}', E_3'', P_{12}', E_4'', P_{13}', E_5'', P_2'', P_{14}', E_6'', P_{15}', E_7'', P_7'', P_1'', P_0'', Q'', R'', S'') → R_1'', p_6'', s'', t'', u'', v'', w'', y'', i'', w'_1', h'', v'_1', p_5'', f'', u'_1', g'', t'_1', e'', s'_1', d'', r'_1', c'', q'_1', p_4'', b'', p_9', e_1'', p_{10}', e_2'', p_{11}', e_3'', p_{12}', e_4'', p_{13}', p_3'', e_5'', p_{14}', e_6'', p_{15}', e_7'', p_7'', p_2'', p_1'', p_0'', q'', r''