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Describing Reflections of Figures

Describing Reflections of Figures
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2023-02-20 12:14
Coordinate GeometryTransformationGeometric Construction
This example demonstrates how to illustrate reflections of figures on the coordinate plane. The core math concepts involved are reflections of figures across a line. Constructed using GeoGebra commands/objects like Shuffle, Element, If, Mod, Vector, Translate, LineBisector, Rotate, Mirror, Polygon, Corner, Segment, Zip, Point, Line, IntersectPath, Intersect, Text, circlePixels. Suitable for grades 6-8 to learn how to describe reflections of figures.

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[40]) → randomList2, {26, 2, 34, 40, 35, 12, 22, 25, 5, 4, 3, 19, 15, 37, 30, 7, 24, 14, 1, 16, 8, 17, 33, 11, 32, 9, 38, 31, 18, 10, 39, 13, 36, 27, 23, 21, 20, 6, 28, 29}
  2. Element(randomList2, Mod[countQuestion, 40] + 1) → randomNum2
  3. Shuffle(Sequence[20]) → randomList1, {15, 3, 5, 19, 1, 20, 12, 17, 11, 13, 14, 10, 8, 9, 6, 4, 18, 2, 16, 7}
  4. Shuffle(Sequence[15]) → randomList3, {5, 13, 9, 3, 12, 10, 7, 1, 2, 4, 15, 6, 11, 8, 14}
  5. Element(randomList3, Mod[countQuestion, 15] + 1) → randomNum3
  6. Element(listYCoordInitCenter, Mod[randomNum3, Length[listYCoordInitCenter]] + 1) → yInitCenter
  7. Shuffle(Sequence[15]) → randomList5, {15, 9, 10, 6, 7, 11, 8, 1, 14, 3, 12, 13, 5, 4, 2}
  8. Element(randomList5, Mod[countQuestion, 15] + 1) → randomNum5
  9. If(Mod[randomNum1, 2] ≟ 1, yInitCenter, Element[listYCoordImgCenter, Mod[randomNum5, Length[listYCoordImgCenter]] + 1]) → yInitCenterImg
  10. Element(listXCoordInitCenter, Mod[randomNum2, Length[listXCoordInitCenter]] + 1) → xInitCenter
  11. Shuffle(Sequence[15]) → randomList4, {7, 12, 15, 2, 10, 1, 6, 8, 11, 9, 14, 3, 4, 13, 5}
  12. Element(randomList4, Mod[countQuestion, 15] + 1) → randomNum4
  13. If(Mod[randomNum1, 2] ≟ 0, xInitCenter, Element[listXCoordImgCenter, Mod[randomNum4, Length[listXCoordImgCenter]] + 1]) → xInitCenterImg
  14. Shuffle(Sequence[15]) → randomList6, {4, 7, 14, 8, 1, 12, 5, 9, 2, 3, 10, 6, 15, 11, 13}
  15. Mod(Element[randomList6, Mod[countQuestion, 15] + 1], 4) → randomNum6
  16. Vector(CenterPoint, (xInitCenter, yInitCenter)) → vectorInitial
  17. Translate(CenterPoint, vectorInitial) → CenterPointPre
  18. LineBisector(CenterPointPre, CenterPointImg) → lineReflection
  19. Rotate(Translate[listBasicVertices(randomNum1), vectorInitial], (90° * randomNum6), CenterPointPre) → verticesPre
  20. Mirror(verticesPre, lineReflection) → verticesImg
  21. Shuffle(Sequence[15]) → randomList7, {5, 4, 9, 1, 12, 3, 11, 6, 10, 8, 13, 2, 14, 15, 7}
  22. 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
  23. Corner(5) → layoutAppSize
  24. Polygon({(16, 9), (-16, 9), (-16, -9), (16, -9)}) → viewBox
  25. Segment((-15.9, 0), (15.9, 0)) → axisX
  26. Segment((0, -8.9), (0, 8.9)) → axisY
  27. Polygon(verticesPre) → FigurePre
  28. Polygon(verticesImg) → FigureImg
  29. Zip(FromTo[AA, BB, timer], AA, verticesPre, BB, verticesImg) → verticesSt
  30. Polygon(verticesSt) → FigureSt
  31. Point(Sequence[Sequence[(a, b), a, -8, 8], b, -8, 8]) → Input1
  32. Point(Sequence[Sequence[(a, b), a, -8, 8], b, -8, 8]) → Input2
  33. Line(Input1, Input2) → lineReflectionStAux
  34. Zip(Segment[AA, BB], AA, verticesPre, BB, verticesSt) → dashedSegments
  35. IntersectPath(lineReflectionStAux, viewBox) → lineReflectionSt
  36. IntersectPath(lineReflection, viewBox) → lineReflectionArrows
  37. Intersect(Circle[CenterPointPre, Distance[CenterPointPre, A] + 0.7], Ray[CenterPointPre, A]) → posLblPointPre,
  38. Mirror(posLblPointPre, lineReflection) → posLblPointImg
  39. Text("A^\prime", posLblPointImg, false, true, 0, 0) → lblA'
  40. Text("A", posLblPointPre, false, true, 0, 0) → lblA
  41. circlePixels(Input2, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject

AI Drawing Prompt Reference

Draw a figure and its reflection across a line. First, determine the vertices of the original figure, then find the reflected vertices through rotation and translation. Next, draw the original figure and its reflection. Finally, draw segments connecting original vertices to their reflections and label them.
The prompt above was compiled from the original drawing commands and is for reference only.