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Triangle Rotations on the Coordinate Plane

Triangle Rotations on the Coordinate Plane
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2023-01-10 11:22
TriangleCoordinate GeometryTransformationGeometric Construction
Explore triangle rotations on the coordinate plane with animations of different directions, angles, and centers of rotation. Core math concepts include rotation, coordinate transformation, and geometric transformations. Constructed using GeoGebra commands like Rotate, UnitOrthogonalVector, Angle. Suitable for grades 6-8 learning coordinate geometry and transformations.

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[100]) → randomList2, {41, 64, 98, 6, 11, 34, 90, 18, 29, 82, 72, 21, 88, 52, 36, 86, 10, 33, 22, 62, 89, 32, 26, 37, 73, 74, 27, 15, 80, 65, 95, 45, 99, 13, 50, 58, 91, 44, 1, 51, 2, 16, 47, 79, 9, 60, 55, 85, 78, 25, 48, 43, 92, 38, 28, 19, 69, 87, 57, 35, 49, 30, 97, 20, 75, 70, 42, 68, 46, 61, 24, 81, 39, 100, 76, 7, 4, 59, 54, 83, 5, 8, 77, 93, 14, 12, 56, 67, 40, 53, 71, 3, 23, 66, 17, 96, 94, 31, 63, 84}
  2. Shuffle(Sequence[100]) → randomList1, {54, 48, 30, 63, 96, 57, 84, 51, 15, 2, 92, 10, 45, 77, 68, 100, 72, 87, 7, 55, 80, 37, 22, 56, 4, 67, 61, 62, 60, 89, 32, 43, 58, 12, 71, 38, 31, 65, 70, 49, 66, 1, 11, 3, 53, 9, 46, 36, 23, 28, 79, 18, 52, 35, 25, 99, 14, 78, 6, 19, 16, 93, 97, 39, 59, 24, 90, 21, 20, 91, 69, 94, 5, 26, 64, 73, 85, 82, 95, 40, 8, 13, 86, 76, 34, 88, 98, 41, 81, 50, 75, 17, 27, 83, 29, 47, 42, 44, 33, 74}
  3. Zip((("$\text{" * A) * "}$"), A, {"90^\circ ", "180^\circ", "270^\circ"}) → selectAngle
  4. SelectedIndex(selectAngle) → selectedAngle
  5. Zip((("$\text{" * A) * " }$"), A, {"clockwise", "counterclockwise"}) → selectDirection
  6. SelectedIndex(selectDirection) → selectedDirection
  7. Flatten(Sequence[Sequence[(i, j), i, -10, 10], j, -10, 10]) → gridPoints
  8. Element(randomList1, Mod[countQuestion, Length[randomList1]] + 1) → randomNum1
  9. Element({verticesCase1(indexCase1), verticesCase2(indexCase2), verticesCase3(indexCase3)}, caseNum) → currentVertices
  10. ClosestPoint(gridPoints, TriangleCenter[currentVertices(1), currentVertices(2), currentVertices(3), 1]) → CenterCase2
  11. Element({(0, 0), CenterCase2, centersCase3(indexCase3)}, caseNum) → RotationPoint
  12. Element(randomList2, Mod[countQuestion, Length[randomList2]] + 1) → randomNum2
  13. Corner(5) → layoutAppSize
  14. Polygon({(-10.5, -10.5), (-10.5, 10.5), (10.5, 10.5), (10.5, -10.5)}) → viewbox
  15. Zip(Vector[UnitVector[Vector[CenterCase2, A]]], A, currentVertices) → vLabels
  16. Polygon(currentVertices) → triABC
  17. Rotate(triABC, (slideRotate * rotateAngle°), RotationPoint) → rotationTriangle
  18. Zip(Distance[RotationPoint, A], A, currentVertices) → distanceToCenter
  19. IndexOf(Max[distanceToCenter], distanceToCenter) → whichIndex
  20. Sequence(Vertex[rotationTriangle, A], A, 1, 3) → rotatedVertices
  21. Zip(Vector[Rotate[A, rotateDegrees°, RotationPoint]], Vector[A], vLabels) → vLabelsRotated
  22. Angle(currentVertices(whichIndex), RotationPoint, rotatedVertices(whichIndex)) → showAngleCounterClockwise
  23. Angle(rotatedVertices(whichIndex), RotationPoint, currentVertices(whichIndex)) → showAngleClockwise
  24. UnitOrthogonalVector(Segment[RotationPoint, rotatedVertices(whichIndex)]) → vArrow
  25. Zip(Text[("" * A), B + C, false, true, 0, 0], A, {"A", "B", "C"}, B, currentVertices, Vector[C], vLabels) → labelsABC
  26. Zip(Text[("" * A), B + C, false, true, 0, 0], A, {"A^{\prime}", "B^{\prime}", "C^{\prime}"}, B, rotatedVertices, Vector[C], vLabelsRotated) → labelsABCPrime
  27. CircleArc(RotationPoint, If[¬clockwiseDirection, currentVertices(whichIndex), rotatedVertices(whichIndex)], If[¬clockwiseDirection, rotatedVertices(whichIndex), currentVertices(whichIndex)]) → displayRotation
  28. Segment(rotatedVertices(whichIndex) + (If[¬clockwiseDirection, -1, 1] * vArrow), rotatedVertices(whichIndex)) → directionArrow
  29. Segment((-10.5, 0), (10.5, 0)) → axisSegmentX
  30. Segment((0, -10.5), (0, 10.5)) → axisSegmentY
  31. Text("y", (0, 11), true, true, 0, 0) → lblY
  32. Text("x", (11.3, 0), true, true, 0, 0) → lblX

AI Drawing Prompt Reference

Draw a triangle on a coordinate plane and show its rotation animation. The figure includes an initial triangle, a rotated triangle, a rotation center, angle indicators, and direction arrows. The construction order is: first draw the coordinate plane and grid, then place the initial triangle, determine the rotation center, rotate the triangle, display the rotation angle and direction, and finally add labels and arrows to explain the rotation process.
The prompt above was compiled from the original drawing commands and is for reference only.