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Deriving the Perimeter of a Rectangle

Deriving the Perimeter of a Rectangle
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2023-09-02 16:36
PolygonCoordinate GeometryGeometric ConstructionSlider Animation
This activity visually demonstrates how to derive the perimeter formula for a rectangle by manipulating vertices. It helps students understand the relationship between perimeter and side lengths. Key math concepts include perimeter calculation and algebraic formula derivation. GeoGebra commands used are Polygon, Segment, Vector, and Translate. Suitable for upper elementary students to develop modeling skills and grasp the perimeter formula.

GeoGebra Commands & Parameters

  1. Mirror(P1, yAxis) → P1'
  2. Mirror(P1', xAxis) → P1''
  3. Mirror(P1'', yAxis) → P1'''
  4. Polygon(P1, P1', P1'', P1''') → peep, p1, p1', p1'', p1'''
  5. Mirror(D, yAxis) → D'
  6. Mirror(D', xAxis) → D''
  7. Mirror(D'', yAxis) → D'''
  8. Polygon(D, D', D'', D''') → q1, d, d', d'', d'''
  9. Dilate(D, If[0 < aniSli ≤ 1, 1 - aniSli, 0], D') → R1
  10. Segment(D, R1) → base1
  11. Dilate(D', If[1 < aniSli ≤ 2, 2 - aniSli, 0], D'') → R2
  12. Segment(D', R2) → heig1
  13. Dilate(D'', If[2 < aniSli ≤ 3, 3 - aniSli, 0], D''') → R3
  14. Segment(D'', R3) → base2
  15. Dilate(D''', If[3 < aniSli ≤ 4, 4 - aniSli, 0], D) → R4
  16. Segment(D''', R4) → heig2
  17. Vector(A, B) → vl1
  18. Vector(C, B) → vl2
  19. Polygon(Corner[textEll1, 1] + (-0.5, 0.7), Corner[textEll1, 2] + (-0.5, 0.7), Corner[textEll1, 3] + (-0.5, 0.7), Corner[textEll1, 4] + (-0.5, 0.7)) → poliEll1, f, g, h, i
  20. Polygon(Corner[textEll2, 1] + (-0.4, 0.7), Corner[textEll2, 2] + (-0.4, 0.7), Corner[textEll2, 3] + (-0.4, 0.7), Corner[textEll2, 4] + (-0.4, 0.7)) → poliEll2, j, k, l, m
  21. Polygon(Corner[textW2, 1] + (-0.6, 0.6), Corner[textW2, 2] + (-0.6, 0.6), Corner[textW2, 3] + (-0.6, 0.6), Corner[textW2, 4] + (-0.6, 0.6)) → poliW2, n, p, q, r
  22. Polygon(Corner[textW1, 1] + (-0.6, 0.6), Corner[textW1, 2] + (-0.6, 0.6), Corner[textW1, 3] + (-0.6, 0.6), Corner[textW1, 4] + (-0.6, 0.6)) → poliW1, s, t, a, b
  23. Vector(E, F) → vw1
  24. Vector(G, F) → vw2
  25. Translate(poliEll1, Vector[(vl1 * If[4 ≤ aniSli ≤ 5, aniSli - 4, 0])]) → poliEll1'
  26. Translate(poliEll2, Vector[(vl2 * If[4 ≤ aniSli ≤ 5, aniSli - 4, 0])]) → poliEll2'
  27. Translate(poliW1, Vector[(vw1 * If[6 ≤ aniSli ≤ 7, aniSli - 6, 0])]) → poliW1'
  28. Translate(poliW2, Vector[(vw2 * If[6 ≤ aniSli ≤ 7, aniSli - 6, 0])]) → poliW2'
  29. Polygon(Corner[text2Ell, 1] + (-0.5, 0.7), Corner[text2Ell, 2] + (-0.5, 0.7), Corner[text2Ell, 3] + (-0.5, 0.7), Corner[text2Ell, 4] + (-0.5, 0.7)) → poli2Ell, c, e, f_1, g_1
  30. Polygon(Corner[text2W, 1] + (-0.5, 0.7), Corner[text2W, 2] + (-0.5, 0.7), Corner[text2W, 3] + (-0.5, 0.7), Corner[text2W, 4] + (-0.5, 0.7)) → poli2W, h_1, i_1, j_1, k_1
  31. Vector(H, I) → vTwoL
  32. Vector(J, I) → vTwoW
  33. Translate(poli2Ell, Vector[(vTwoL * If[8 ≤ aniSli ≤ 9, aniSli - 8, 0])]) → poli2Ell'
  34. Translate(poli2W, Vector[(vTwoW * If[8 ≤ aniSli ≤ 9, aniSli - 8, 0])]) → poli2W'

AI Drawing Prompt Reference

Draw a rectangle and generate multiple scaled rectangles using scaling. Use vectors and translation to create other graphics. The figure includes rectangles, scaled rectangles, vectors, and translated graphics.
The prompt above was compiled from the original drawing commands and is for reference only.