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Kite Perimeter and Rotation Demo

Kite Perimeter and Rotation Demo
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2015-11-12 23:05
PolygonVectorTransformationGeometric ConstructionSlider Animation
In collections CCSS Support Math I Unit 6
① This example demonstrates the geometric construction of a kite (convex quadrilateral), the calculation of its perimeter, and a dynamic rotation about a fixed point. ② Core mathematical concepts include kite properties, perimeter formula, vector representation, rotation transformations, and sequence/slider‑driven animation. ③ Construction highlights: Circle, Point, Segment, and Intersect create vertices and edges; Vector defines edge vectors; Sequence together with Slider1 and Slider2 controls the rotation angle and generates the animated trace; LaTeX labels dimensions and formulas; UI objects such as Progressbar and Hint support interactive teaching. ④ Suitable for middle‑school geometry (quadrilaterals, perimeter), high‑school vectors and transformations, and as a GeoGebra geometric construction and slider animation teaching resource.

GeoGebra Commands & Parameters

  1. Circle(C, Slider1) → c
  2. Point(c) → D
  3. Segment((0, 0), (0, 1)) → i
  4. Segment(A_0, B_0) → Scaleline
  5. Sequence(Segment[A_0 + (i, 0), A_0 + (i, (-0.5))], i, 0, 10) → list1
  6. Sequence(Segment[A_0 + (i - 0.5, 0), A_0 + (i - 0.5, (-0.4))], i, 1, 10) → list2
  7. Sequence(Sequence[Segment[A_0 + ((0.5 * i) + (0.1 * j), 0), A_0 + ((0.5 * i) + (0.1 * j), (-0.3))], j, 1, 4], i, 0, 19) → list3
  8. Segment(D_0, (x(D_0), 0)) → j
  9. Vector(C_0, D_0) → u
  10. LaTeX("\text{Hank made a kite to fly in the local kite festival. The dimensions of his kite are shown in the following diagram.}") → text1
  11. LaTeX("\text{If Hank wants to put trim around the edges of his kite, how much trim does he need?}") → text2
  12. LaTeX("\text{Determine the length of each side.}") → text3
  13. LaTeX("\text{Find the perimeter.}") → text6
  14. LaTeX("\text{To find the perimeter, add the lengths of all the sides.}") → text7
  15. LaTeX("\text{Write an equation.}") → text9
  16. LaTeX("\text{Simplify.}") → text11
  17. Segment(C, D) → b
  18. Point(c) → E
  19. Segment(C, E) → d
  20. Circle(D, Slider2) → e
  21. Circle(E, Slider2) → f
  22. Intersect(e, f, 1) → F
  23. Segment(D, F) → g
  24. Segment(F, E) → l
  25. LaTeX("\text{0}") → Scalevalue0
  26. LaTeX("\text{10}") → Scalevalue1
  27. LaTeX("\text{20}") → Scalevalue2
  28. LaTeX("\text{30}") → Scalevalue3
  29. LaTeX("\text{40}") → Scalevalue4
  30. LaTeX("\text{50}") → Scalevalue5
  31. LaTeX("\text{60}") → Scalevalue6
  32. LaTeX("\text{70}") → Scalevalue7
  33. LaTeX("\text{80}") → Scalevalue8
  34. LaTeX("\text{90}") → Scalevalue9
  35. LaTeX("\text{100}") → Scalevalue10
  36. Segment(G, H) → h
  37. Vector(H, P1) → v
  38. Segment(P1, (x(P1), 0)) → k
  39. LaTeX((("\text{The sides marked with one tick mark are both \textcolor{#000099}{" * v1) * "} inches long.}")) → text4
  40. LaTeX((("\text{The sides marked with two tick marks are both \textcolor{#000099}{" * v2) * "} inches long.}")) → text5
  41. LaTeX((((((((("\text{\textcolor{#000099}{P = " * v1) * "+") * v1) * "+") * v2) * "+") * v2) * "}}")) → text8
  42. LaTeX((("\text{\textcolor{#000099}{P = " * sol) * "}}")) → text10
  43. LaTeX("\text{of trim.}") → text12_1
  44. LaTeX((((("\text{The perimeter of the kite is \textcolor{#000099}{" * sol) * "} inches; therefore, Hank will need \textcolor{#000099}{") * sol) * "} inches }")) → text12
  45. LaTeX("\text{\mathbf{Perimeter} the distance around a two-dimensional figure.}") → text13
  46. LaTeX("\text{\mathbf{Line\; segment} a part of a line that is noted by two endpoints,(x ,y ) and (x ,y ). }") → text14

AI Drawing Prompt Reference

Draw a kite diagram, a convex quadrilateral with two equal symmetric sides. Include a fixed rotation center, one vertex rotating around it, and a slider controlling the rotation angle, with the rotation trajectory drawn as line segments. Connect the four kite vertices and edges with line segments. The construction order should be: first establish the initial kite shape and rotation center, then add the slider to control rotation angle, and finally draw the rotation trajectory. The diagram should clearly show the kite's geometric structure, rotation transformation, and dynamic animation.
The prompt above was compiled from the original drawing commands and is for reference only.