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Point-by-Point Transformation Practice

Point-by-Point Transformation Practice
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2020-11-19 23:37
PolygonCoordinate GeometryTransformationGeometric Construction
This example demonstrates the process of drawing shapes through point-by-point transformations. It involves core mathematical concepts such as transformations, coordinate geometry, and polygon construction. Key GeoGebra commands used include Sequence, Join, Polygon, RemoveUndefined, Point, PolyLine, Line, and Intersect. Suitable for middle school and above students learning and practicing geometric transformations.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[(p, q), p, ceil(x(S)), floor(x(T)), px], q, ceil(y(T)), floor(y(S)), py) → list2
  2. Join(Sequence[Sequence[(p * U) + (q * V), p, (-m), m, px1], q, (-m), m, py1]) → list1
  3. Polygon(S, (x(S), y(T)), T, (x(T), y(S))) → poly2, c, d, e, f
  4. RemoveUndefined(Sequence[If[IsInRegion[Element[list1, k], poly2], Element[list1, k], (NaN, NaN)], k, 1, Length[list1]]) → liste1
  5. Point(liste1) → A
  6. Point(liste1) → B
  7. Point(liste1) → C
  8. PolyLine(A, B, C) → g
  9. Point(liste1) → D
  10. Point(liste1) → E
  11. Point(liste1) → F
  12. PolyLine(D, E, F) → h
  13. Point(liste1) → G_1
  14. Point(liste1) → H_1
  15. Polygon(G_1, H_1, 6) → poly1, i, L_1, j, k, l, n, p, I_1, J_1, K_1
  16. Point(liste1) → B_1
  17. Point(liste1) → C_1
  18. Line(B_1, C_1) → h_1
  19. Point(liste1) → M_1
  20. Point(liste1) → O_1
  21. Line(M_1, O_1) → q
  22. Line(P_1, N_1) → r
  23. Point(liste1) → Q_1
  24. Point(liste1) → R_1
  25. Line(Q_1, R_1) → s
  26. Intersect(h_1, r) → W
  27. Intersect(h_1, s) → Z
  28. Polygon(W, Z, 6) → poly3, t, F_1, f_1, g_1, i_1, j_1, k_1, A_1, D_1, E_1

AI Drawing Prompt Reference

Create a geometric practice diagram based on point transformations. Start with a rectangle defined by two reference points and their coordinate projections. Generate a grid of points inside this rectangle, then filter to keep only those within the rectangle. From these points, select several groups to form polylines, polygons, and lines. Two lines intersect at a point, and with another point, construct a regular hexagon. The final figure includes grid points, polylines, polygons, lines, and a hexagon, illustrating transformations and geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.