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Describing Rotations of Figures

Describing Rotations of Figures
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2023-03-03 11:27
PolygonVectorCoordinate GeometryTransformationGeometric Construction
This exploration activity allows students to rotate figures and learn how to describe the transformation. It involves core math concepts like rigid transformations, specifically rotations. Constructed using GeoGebra commands such as Sequence, Circle, Point, Angle, If, Shuffle, Element, Mod, Vector, Translate, KeepIf, Join, Rotate, Textfield, Polygon, Corner, Segment. Suitable for grades 6-8 learning transformations in coordinate geometry.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[D, n°, B], n, 1, 360) → dialPoints
  2. Circle(B, 3) → dial
  3. Point(dialPoints) → C
  4. Angle(D, B, C) → alpha
  5. If(clockwise, 1, 2) → senseCase
  6. Shuffle(Sequence[100]) → randomList8, {72, 50, 38, 13, 2, 44, 99, 100, 75, 98, 71, 89, 87, 25, 37, 84, 58, 29, 11, 51, 7, 47, 8, 81, 65, 28, 54, 16, 26, 19, 90, 49, 68, 20, 76, 55, 27, 9, 61, 33, 91, 34, 53, 59, 17, 41, 62, 64, 57, 82, 86, 78, 32, 24, 1, 15, 3, 4, 79, 67, 22, 31, 93, 6, 83, 48, 56, 95, 60, 52, 14, 66, 10, 23, 63, 5, 21, 70, 12, 80, 74, 94, 42, 88, 36, 96, 73, 45, 69, 35, 85, 30, 39, 43, 40, 18, 92, 97, 77, 46}
  7. Shuffle(Sequence[15]) → randomList2, {2, 8, 11, 3, 6, 12, 10, 15, 1, 7, 4, 5, 9, 14, 13}
  8. Shuffle(Sequence[15]) → randomList6, {15, 12, 10, 7, 6, 14, 11, 9, 4, 8, 2, 3, 5, 1, 13}
  9. Element(randomList2, Mod[countQuestion, 15] + 1) → randomNum2
  10. Mod(Element[randomList6, Mod[countQuestion, 15] + 1], 4) → randomNum6
  11. Shuffle(Sequence[20]) → randomList1, {14, 3, 1, 9, 7, 4, 11, 12, 2, 6, 18, 8, 16, 10, 19, 5, 13, 20, 15, 17}
  12. Element(listCoordInitCenter, Mod[randomNum2, Length[listCoordInitCenter]] + 1) → xInitCenter
  13. Shuffle(Sequence[15]) → randomList3, {5, 1, 10, 14, 6, 7, 15, 4, 8, 12, 3, 13, 11, 2, 9}
  14. Element(randomList3, Mod[countQuestion, 15] + 1) → randomNum3
  15. Element({pi / 2, pi, ((-pi)) / 2}, Mod[randomNum3, 3] + 1) → angleImg
  16. Element(listCoordInitCenter, Mod[randomNum3, Length[listCoordInitCenter]] + 1) → yInitCenter
  17. Vector(CenterPoint, (xInitCenter, yInitCenter)) → vectorInitial
  18. Translate(CenterPoint, vectorInitial) → CenterPointPre
  19. KeepIf(CenterOKNew[PP, angleImg, CenterPointPre, radiusFig], PP, Flatten[Zip[Zip[(j, k), j, listCoordInitCenter], k, listCoordInitCenter] \ {CenterPointPre}]) → listCentersImgCandidates
  20. Element(listCentersImgCandidates, Mod[randomList8(1), Length[listCentersImgCandidates]] + 1) → RandomCenter
  21. Join({{CenterPointPre, (0, 0)}, {RandomCenter}}) → listCentersImg
  22. Rotate(Translate[listBasicVertices(randomNum1), vectorInitial], (90° * randomNum6), CenterPointPre) → verticesPre
  23. Shuffle(Sequence[15]) → randomList5, {12, 6, 3, 13, 8, 9, 2, 1, 11, 14, 5, 10, 15, 7, 4}
  24. Element(randomList5, Mod[countQuestion, 15] + 1) → randomNum5
  25. Element(listCentersImg, Mod[randomNum5, 3] + 1) → CenterRot
  26. Shuffle(Sequence[15]) → randomList4, {14, 9, 1, 10, 2, 5, 15, 11, 13, 3, 4, 6, 7, 12, 8}
  27. Element(randomList4, Mod[countQuestion, 15] + 1) → randomNum4
  28. Element(listCoordInitCenter \ Sequence[xInitCenter - 2, xInitCenter + 2], Mod[randomNum4, Length[listCoordInitCenter \ Sequence[xInitCenter - 2, xInitCenter + 2]]] + 1) → xInitCenterImg
  29. Element(listCoordInitCenter \ Sequence[yInitCenter - 2, yInitCenter + 2], Mod[randomNum5, Length[listCoordInitCenter \ Sequence[yInitCenter - 2, yInitCenter + 2]]] + 1) → yInitCenterImg
  30. Shuffle(Sequence[15]) → randomList7, {14, 4, 7, 6, 13, 3, 2, 8, 12, 10, 15, 5, 11, 1, 9}
  31. Textfield(input1) → InputBox1
  32. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  33. Corner(5) → layoutAppSize
  34. Polygon({(9, 9), (-9, 9), (-9, -9), (9, -9)}) → viewBox
  35. Segment((-8.9, 0), (8.9, 0)) → axisX
  36. Segment((0, -8.9), (0, 8.9)) → axisY
  37. Polygon(verticesPre) → FigurePre
  38. Rotate(verticesPre, angleImg, CenterRot) → verticesImg
  39. Polygon(verticesImg) → FigureImg
  40. Rotate(verticesPre, (-input1), CenterRot) → verticesSt
  41. Polygon(verticesSt) → FigureSt
  42. Element({(("\color{" * colorPink) * "}clockwise"), (("\color{" * colorPurpleDark) * "}counterclockwise")}, senseCase) → sense
  43. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  44. circlePixels(D, 10 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject

AI Drawing Prompt Reference

Draw a coordinate-plane rotation scene. First place a rotation center point and draw the x- and y-axes as the horizontal and vertical segments through the origin. Construct a reference circle centered at a point associated with the rotation setup, with radius 3. Build a polygon as the original rigid figure using generated vertices, then rotate the polygon around the rotation center by a chosen angle taken from {90°, 180°, −90°} to obtain the rotated figure. Show the rotation angle with an angle arc and angle label formed by two rays starting at the same vertex, and add a short text cue indicating whether the rotation is clockwise or counterclockwise.
The prompt above was compiled from the original drawing commands and is for reference only.