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Describing Horizontal and Vertical Translations of Figures

Describing Horizontal and Vertical Translations of Figures
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2023-02-13 21:35
VectorCoordinate GeometryTransformationGeometric Construction
This example demonstrates how to translate figures horizontally and vertically on the coordinate plane. Key math concepts include rigid transformations, translations, and coordinate geometry. Construction highlights: Utilizes GeoGebra commands like Shuffle, Vector, Mod, Element, Translate, Rotate, Textfield, Polygon, Corner, Segment, Intersect, Text; objects include input2, listBasicVertices, randomList6, input1, vectorSt, listCenters, countQuestion, randomNum6, randomList2, randomNum2, randomList1, randomNum1, CenterPoint, radios, radiusFig, listCoordInitCenter, xInitCenter, randomList3, randomNum3, yInitCenter, vectorInitial, CenterPointPre, verticesPre, randomList4, randomNum4, yInitCenterImg, xInitCenterImg, CenterPointImg, xMax, yMin, randomList7, vectorTransl, randomList5, randomNum5, colorGreyDark, btnNew, InputBox1, correct, scriptResetApp, colorTealSuccess. Suitable for grades 6-8, focusing on describing rigid transformations of plane figures.

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[15]) → randomList6, {1, 3, 14, 9, 7, 6, 15, 8, 4, 13, 10, 12, 5, 2, 11}
  2. Vector((input1, input2)) → vectorSt
  3. Mod(Element[randomList6, Mod[countQuestion, 15] + 1], 4) → randomNum6
  4. Shuffle(Sequence[15]) → randomList2, {3, 2, 14, 12, 7, 15, 6, 8, 4, 10, 9, 5, 13, 1, 11}
  5. Element(randomList2, Mod[countQuestion, 15] + 1) → randomNum2
  6. Shuffle(Sequence[20]) → randomList1, {4, 8, 14, 6, 9, 13, 2, 3, 1, 20, 17, 5, 15, 16, 10, 7, 11, 18, 12, 19}
  7. Element(listCoordInitCenter, Mod[randomNum2, Length[listCoordInitCenter]] + 1) → xInitCenter
  8. Shuffle(Sequence[15]) → randomList3, {15, 5, 2, 7, 12, 14, 3, 1, 4, 13, 11, 10, 8, 6, 9}
  9. Element(randomList3, Mod[countQuestion, 15] + 1) → randomNum3
  10. Element(listCoordInitCenter, Mod[randomNum3, Length[listCoordInitCenter]] + 1) → yInitCenter
  11. Vector(CenterPoint, (xInitCenter, yInitCenter)) → vectorInitial
  12. Translate(CenterPoint, vectorInitial) → CenterPointPre
  13. Rotate(Translate[listBasicVertices(randomNum1), vectorInitial], (90° * randomNum6), CenterPointPre) → verticesPre
  14. Shuffle(Sequence[15]) → randomList4, {7, 5, 4, 6, 3, 9, 14, 13, 2, 11, 15, 12, 8, 1, 10}
  15. Element(randomList4, Mod[countQuestion, 15] + 1) → randomNum4
  16. Element(listCoordInitCenter \ Sequence[yInitCenter - 2, yInitCenter + 2], Mod[randomNum4, Length[listCoordInitCenter \ Sequence[yInitCenter - 2, yInitCenter + 2]]] + 1) → yInitCenterImg
  17. Element(listCoordInitCenter \ Sequence[xInitCenter - 2, xInitCenter + 2], Mod[randomNum4, Length[listCoordInitCenter \ Sequence[xInitCenter - 2, xInitCenter + 2]]] + 1) → xInitCenterImg
  18. Shuffle(Sequence[15]) → randomList7, {10, 4, 1, 8, 14, 6, 5, 3, 11, 2, 13, 9, 12, 15, 7}
  19. Vector(CenterPointPre, CenterPointImg) → vectorTransl
  20. Shuffle(Sequence[15]) → randomList5, {4, 2, 15, 7, 12, 14, 13, 6, 10, 11, 9, 8, 5, 3, 1}
  21. Element(randomList5, Mod[countQuestion, 15] + 1) → randomNum5
  22. Textfield(input1) → InputBox1
  23. 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
  24. Corner(5) → layoutAppSize
  25. Polygon({(9, 9), (-9, 9), (-9, -9), (9, -9)}) → viewBox
  26. Segment((-9, 0), (9, 0)) → axisX
  27. Segment((0, -9), (0, 9)) → axisY
  28. Polygon(verticesPre) → FigurePre
  29. Translate(verticesPre, vectorTransl) → verticesImg
  30. Polygon(verticesImg) → FigureImg
  31. Translate(verticesPre, vectorSt) → verticesSt
  32. Polygon(verticesSt) → FigureSt
  33. Intersect(Circle[CenterPointPre, Distance[CenterPointPre, A] + 0.8], Ray[CenterPointPre, A]) → posLblPointPre,
  34. Translate(posLblPointPre, vectorTransl) → posLblPointImg
  35. Text("A", posLblPointPre, false, true, 0, 0) → lblA
  36. Text("A^\prime", posLblPointImg, false, true, 0, 0) → lblA'

AI Drawing Prompt Reference

Draw a planar figure on a Cartesian coordinate grid together with the coordinate axes and a defined view frame. Construct an initial polygon from a given set of vertices, then place the figure and its translated image by using a horizontal/vertical translation vector. Next, create a second configuration by using vertices derived from a rotation about a center point, and then translate those vertices again using another translation vector so that the moved figure appears in a new location. Show two corresponding marked points near the start and end positions, labeling them as A and A′ to indicate the relationship between the original and translated/rotated figures.
The prompt above was compiled from the original drawing commands and is for reference only.