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Point Transformation

Point Transformation
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2026-05-15 23:34
VectorFunctionTransformation
In collections complex-numbers
This example demonstrates the transformation of points. Key mathematical concepts include function transformation, vectors, and similarity transformation. Using GeoGebra commands such as Vector, Sequence, and Length, the point transformation effect is constructed. Suitable for middle school students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Vector(A, A + (B - A) / n) → u
  2. Vector(A, A + (C - A) / n) → v
  3. Sequence(Sequence[A + (k * u) + (j * v), k, 0, n, 1 / n], j, 0, n, 1 / n) → m1
  4. Length(m1) → c
  5. Textfield(a) → CampEntradaSortida1
  6. Textfield(b) → CampEntradaSortida2
  7. Sequence(Sequence[(a(x(m1(i, j)), y(m1(i, j))), b(x(m1(i, j)), y(m1(i, j)))), i, 1, tt], j, 1, tt) → m2
  8. Sequence(m1(k, tt), k, 1, c) → l1
  9. Sequence(Segmentparamètric[Element[m1, k, 1], Element[m1, k, c]], k, 1, tt) → l2
  10. Sequence(Segmentparamètric[Element[m1, 1, k], Element[m1, c, k]], k, 1, tt) → l3
  11. Element(l2, A1) → B1
  12. Element(l2, A2) → B2
  13. Element(l2, A3) → B3
  14. Element(l2, A4) → B4
  15. Element(l2, A5) → B5
  16. Element(l2, A6) → B6
  17. Element(l2, A7) → B7
  18. Element(l2, A8) → B8
  19. Element(l2, A9) → B9
  20. Element(l2, A10) → B10
  21. Element(l2, A11) → B11
  22. Element(l2, A12) → B12
  23. Element(l2, A13) → B13
  24. Element(l2, A14) → B14
  25. Element(l2, A15) → B15
  26. Element(l2, A16) → B16
  27. Element(l2, A17) → B17
  28. Element(l2, A18) → B18
  29. Element(l2, A19) → B19
  30. Element(l2, A20) → B20
  31. Element(l2, A21) → B21
  32. Element(l2, A22) → B22
  33. Element(l2, A23) → B23
  34. Element(l2, A24) → B24
  35. Element(l2, A25) → B25
  36. Element(l2, A26) → B26
  37. Element(l2, A27) → B27
  38. Element(l2, A28) → B28
  39. Element(l2, A29) → B29
  40. Element(l2, A30) → B30
  41. Element(l2, A31) → B31
  42. Element(l2, A32) → B32
  43. Element(l2, A33) → B33
  44. Element(l2, A34) → B34
  45. Element(l2, A35) → B35
  46. Element(l2, A36) → B36
  47. Element(l2, A37) → B37
  48. Element(l3, A1) → C1
  49. Element(l3, A2) → C2
  50. Element(l3, A3) → C3
  51. Element(l3, A4) → C4
  52. Element(l3, A5) → C5
  53. Element(l3, A6) → C6
  54. Element(l3, A7) → C7
  55. Element(l3, A8) → C8
  56. Element(l3, A9) → C9
  57. Element(l3, A10) → C10
  58. Element(l3, A11) → C11
  59. Element(l3, A12) → C12
  60. Element(l3, A13) → C13
  61. Element(l3, A14) → C14
  62. Element(l3, A15) → C15
  63. Element(l3, A16) → C16
  64. Element(l3, A17) → C17
  65. Element(l3, A18) → C18
  66. Element(l3, A19) → C19
  67. Element(l3, A20) → C20
  68. Element(l3, A21) → C21
  69. Element(l3, A22) → C22
  70. Element(l3, A23) → C23
  71. Element(l3, A24) → C24
  72. Element(l3, A25) → C25
  73. Element(l3, A26) → C26
  74. Element(l3, A27) → C27
  75. Element(l3, A28) → C28
  76. Element(l3, A29) → C29
  77. Element(l3, A30) → C30
  78. Element(l3, A31) → C31
  79. Element(l3, A32) → C32
  80. Element(l3, A33) → C33
  81. Element(l3, A34) → C34
  82. Element(l3, A35) → C35
  83. Element(l3, A36) → C36
  84. Element(l3, A37) → C37
  85. CurveCartesian(a(x(B1(t)), y(B1(t))), b(x(B1(t)), y(B1(t))), t, 0, 1) → D1
  86. CurveCartesian(a(x(B2(t)), y(B2(t))), b(x(B2(t)), y(B2(t))), t, 0, 1) → D2
  87. CurveCartesian(a(x(B3(t)), y(B3(t))), b(x(B3(t)), y(B3(t))), t, 0, 1) → D3
  88. CurveCartesian(a(x(B4(t)), y(B4(t))), b(x(B4(t)), y(B4(t))), t, 0, 1) → D4
  89. CurveCartesian(a(x(B5(t)), y(B5(t))), b(x(B5(t)), y(B5(t))), t, 0, 1) → D5
  90. CurveCartesian(a(x(B6(t)), y(B6(t))), b(x(B6(t)), y(B6(t))), t, 0, 1) → D6
  91. CurveCartesian(a(x(B7(t)), y(B7(t))), b(x(B7(t)), y(B7(t))), t, 0, 1) → D7
  92. CurveCartesian(a(x(B8(t)), y(B8(t))), b(x(B8(t)), y(B8(t))), t, 0, 1) → D8
  93. CurveCartesian(a(x(B9(t)), y(B9(t))), b(x(B9(t)), y(B9(t))), t, 0, 1) → D9
  94. CurveCartesian(a(x(B10(t)), y(B10(t))), b(x(B10(t)), y(B10(t))), t, 0, 1) → D10
  95. CurveCartesian(a(x(B11(t)), y(B11(t))), b(x(B11(t)), y(B11(t))), t, 0, 1) → D11
  96. CurveCartesian(a(x(B12(t)), y(B12(t))), b(x(B12(t)), y(B12(t))), t, 0, 1) → D12
  97. CurveCartesian(a(x(B13(t)), y(B13(t))), b(x(B13(t)), y(B13(t))), t, 0, 1) → D13
  98. CurveCartesian(a(x(B14(t)), y(B14(t))), b(x(B14(t)), y(B14(t))), t, 0, 1) → D14
  99. CurveCartesian(a(x(B15(t)), y(B15(t))), b(x(B15(t)), y(B15(t))), t, 0, 1) → D15
  100. CurveCartesian(a(x(B16(t)), y(B16(t))), b(x(B16(t)), y(B16(t))), t, 0, 1) → D16
  101. CurveCartesian(a(x(B17(t)), y(B17(t))), b(x(B17(t)), y(B17(t))), t, 0, 1) → D17
  102. CurveCartesian(a(x(B18(t)), y(B18(t))), b(x(B18(t)), y(B18(t))), t, 0, 1) → D18
  103. CurveCartesian(a(x(B19(t)), y(B19(t))), b(x(B19(t)), y(B19(t))), t, 0, 1) → D19
  104. CurveCartesian(a(x(B20(t)), y(B20(t))), b(x(B20(t)), y(B20(t))), t, 0, 1) → D20
  105. CurveCartesian(a(x(B21(t)), y(B21(t))), b(x(B21(t)), y(B21(t))), t, 0, 1) → D21
  106. CurveCartesian(a(x(B22(t)), y(B22(t))), b(x(B22(t)), y(B22(t))), t, 0, 1) → D22
  107. CurveCartesian(a(x(B23(t)), y(B23(t))), b(x(B23(t)), y(B23(t))), t, 0, 1) → D23
  108. CurveCartesian(a(x(B24(t)), y(B24(t))), b(x(B24(t)), y(B24(t))), t, 0, 1) → D24
  109. CurveCartesian(a(x(B25(t)), y(B25(t))), b(x(B25(t)), y(B25(t))), t, 0, 1) → D25
  110. CurveCartesian(a(x(B26(t)), y(B26(t))), b(x(B26(t)), y(B26(t))), t, 0, 1) → D26
  111. CurveCartesian(a(x(B27(t)), y(B27(t))), b(x(B27(t)), y(B27(t))), t, 0, 1) → D27
  112. CurveCartesian(a(x(B28(t)), y(B28(t))), b(x(B28(t)), y(B28(t))), t, 0, 1) → D28
  113. CurveCartesian(a(x(B29(t)), y(B29(t))), b(x(B29(t)), y(B29(t))), t, 0, 1) → D29
  114. CurveCartesian(a(x(B30(t)), y(B30(t))), b(x(B30(t)), y(B30(t))), t, 0, 1) → D30
  115. CurveCartesian(a(x(B31(t)), y(B31(t))), b(x(B31(t)), y(B31(t))), t, 0, 1) → D31
  116. CurveCartesian(a(x(B32(t)), y(B32(t))), b(x(B32(t)), y(B32(t))), t, 0, 1) → D32
  117. CurveCartesian(a(x(B33(t)), y(B33(t))), b(x(B33(t)), y(B33(t))), t, 0, 1) → D33
  118. CurveCartesian(a(x(B34(t)), y(B34(t))), b(x(B34(t)), y(B34(t))), t, 0, 1) → D34
  119. CurveCartesian(a(x(B35(t)), y(B35(t))), b(x(B35(t)), y(B35(t))), t, 0, 1) → D35
  120. CurveCartesian(a(x(B36(t)), y(B36(t))), b(x(B36(t)), y(B36(t))), t, 0, 1) → D36
  121. CurveCartesian(a(x(B37(t)), y(B37(t))), b(x(B37(t)), y(B37(t))), t, 0, 1) → D37
  122. CurveCartesian(a(x(C1(t)), y(C1(t))), b(x(C1(t)), y(C1(t))), t, 0, 1) → E1
  123. CurveCartesian(a(x(C2(t)), y(C2(t))), b(x(C2(t)), y(C2(t))), t, 0, 1) → E2
  124. CurveCartesian(a(x(C3(t)), y(C3(t))), b(x(C3(t)), y(C3(t))), t, 0, 1) → E3
  125. CurveCartesian(a(x(C4(t)), y(C4(t))), b(x(C4(t)), y(C4(t))), t, 0, 1) → E4
  126. CurveCartesian(a(x(C5(t)), y(C5(t))), b(x(C5(t)), y(C5(t))), t, 0, 1) → E5
  127. CurveCartesian(a(x(C6(t)), y(C6(t))), b(x(C6(t)), y(C6(t))), t, 0, 1) → E6
  128. CurveCartesian(a(x(C7(t)), y(C7(t))), b(x(C7(t)), y(C7(t))), t, 0, 1) → E7
  129. CurveCartesian(a(x(C8(t)), y(C8(t))), b(x(C8(t)), y(C8(t))), t, 0, 1) → E8
  130. CurveCartesian(a(x(C9(t)), y(C9(t))), b(x(C9(t)), y(C9(t))), t, 0, 1) → E9
  131. CurveCartesian(a(x(C10(t)), y(C10(t))), b(x(C10(t)), y(C10(t))), t, 0, 1) → E10
  132. CurveCartesian(a(x(C11(t)), y(C11(t))), b(x(C11(t)), y(C11(t))), t, 0, 1) → E11
  133. CurveCartesian(a(x(C12(t)), y(C12(t))), b(x(C12(t)), y(C12(t))), t, 0, 1) → E12
  134. CurveCartesian(a(x(C13(t)), y(C13(t))), b(x(C13(t)), y(C13(t))), t, 0, 1) → E13
  135. CurveCartesian(a(x(C14(t)), y(C14(t))), b(x(C14(t)), y(C14(t))), t, 0, 1) → E14
  136. CurveCartesian(a(x(C15(t)), y(C15(t))), b(x(C15(t)), y(C15(t))), t, 0, 1) → E15
  137. CurveCartesian(a(x(C16(t)), y(C16(t))), b(x(C16(t)), y(C16(t))), t, 0, 1) → E16
  138. CurveCartesian(a(x(C17(t)), y(C17(t))), b(x(C17(t)), y(C17(t))), t, 0, 1) → E17
  139. CurveCartesian(a(x(C18(t)), y(C18(t))), b(x(C18(t)), y(C18(t))), t, 0, 1) → E18
  140. CurveCartesian(a(x(C19(t)), y(C19(t))), b(x(C19(t)), y(C19(t))), t, 0, 1) → E19
  141. CurveCartesian(a(x(C20(t)), y(C20(t))), b(x(C20(t)), y(C20(t))), t, 0, 1) → E20
  142. CurveCartesian(a(x(C21(t)), y(C21(t))), b(x(C21(t)), y(C21(t))), t, 0, 1) → E21
  143. CurveCartesian(a(x(C22(t)), y(C22(t))), b(x(C22(t)), y(C22(t))), t, 0, 1) → E22
  144. CurveCartesian(a(x(C23(t)), y(C23(t))), b(x(C23(t)), y(C23(t))), t, 0, 1) → E23
  145. CurveCartesian(a(x(C24(t)), y(C24(t))), b(x(C24(t)), y(C24(t))), t, 0, 1) → E24
  146. CurveCartesian(a(x(C25(t)), y(C25(t))), b(x(C25(t)), y(C25(t))), t, 0, 1) → E25
  147. CurveCartesian(a(x(C26(t)), y(C26(t))), b(x(C26(t)), y(C26(t))), t, 0, 1) → E26
  148. CurveCartesian(a(x(C27(t)), y(C27(t))), b(x(C27(t)), y(C27(t))), t, 0, 1) → E27
  149. CurveCartesian(a(x(C28(t)), y(C28(t))), b(x(C28(t)), y(C28(t))), t, 0, 1) → E28
  150. CurveCartesian(a(x(C29(t)), y(C29(t))), b(x(C29(t)), y(C29(t))), t, 0, 1) → E29
  151. CurveCartesian(a(x(C30(t)), y(C30(t))), b(x(C30(t)), y(C30(t))), t, 0, 1) → E30
  152. CurveCartesian(a(x(C31(t)), y(C31(t))), b(x(C31(t)), y(C31(t))), t, 0, 1) → E31
  153. CurveCartesian(a(x(C32(t)), y(C32(t))), b(x(C32(t)), y(C32(t))), t, 0, 1) → E32
  154. CurveCartesian(a(x(C33(t)), y(C33(t))), b(x(C33(t)), y(C33(t))), t, 0, 1) → E33
  155. CurveCartesian(a(x(C34(t)), y(C34(t))), b(x(C34(t)), y(C34(t))), t, 0, 1) → E34
  156. CurveCartesian(a(x(C35(t)), y(C35(t))), b(x(C35(t)), y(C35(t))), t, 0, 1) → E35
  157. CurveCartesian(a(x(C36(t)), y(C36(t))), b(x(C36(t)), y(C36(t))), t, 0, 1) → E36
  158. CurveCartesian(a(x(C37(t)), y(C37(t))), b(x(C37(t)), y(C37(t))), t, 0, 1) → E37

AI Drawing Prompt Reference

Draw a point transformation example to demonstrate function transformation, vectors, and similarity transformation. Start by plotting two points, then create two vectors based on these points. Use the vectors to generate a series of points forming a grid. Measure the length of the grid and adjust each point's position based on input parameters a and b, finally drawing the transformed grid and connecting adjacent points with lines to show the transformation effect.
The prompt above was compiled from the original drawing commands and is for reference only.