MathPlotAI Logo MathPlotAI

Describing the Rotation of Triangles

Describing the Rotation of Triangles
Loading the math board and drawing, please wait…
2023-01-11 05:05
TriangleCoordinate GeometryTransformation
This example demonstrates how to describe the rotation of triangles on the coordinate plane. By analyzing the direction, angle, and center of rotation, students can understand the concept of rigid transformations. GeoGebra commands such as Rotate, Angle, and Textfield are used in construction. Suitable for 6-8 grade students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[100]) → randomList1, {47, 50, 61, 12, 35, 67, 94, 74, 76, 45, 98, 65, 25, 86, 19, 55, 85, 84, 93, 8, 26, 73, 52, 57, 75, 18, 69, 63, 37, 96, 88, 48, 1, 54, 62, 42, 17, 90, 6, 59, 39, 99, 77, 36, 16, 13, 23, 44, 71, 4, 43, 21, 70, 92, 32, 31, 80, 14, 79, 72, 38, 29, 100, 9, 5, 2, 28, 49, 78, 60, 24, 20, 95, 87, 15, 33, 68, 56, 91, 58, 53, 46, 22, 89, 30, 51, 3, 10, 64, 11, 97, 41, 34, 81, 82, 27, 40, 83, 7, 66}
  2. Shuffle(Sequence[100]) → randomList2, {12, 30, 39, 71, 65, 22, 63, 92, 44, 97, 76, 81, 55, 96, 58, 24, 26, 70, 91, 36, 15, 41, 48, 99, 68, 73, 50, 84, 18, 86, 13, 7, 11, 90, 85, 31, 93, 10, 37, 57, 33, 62, 88, 95, 17, 20, 78, 60, 3, 9, 43, 35, 79, 75, 2, 51, 87, 77, 59, 19, 34, 29, 16, 69, 32, 4, 46, 49, 5, 47, 25, 100, 94, 8, 40, 6, 28, 1, 82, 27, 23, 54, 66, 56, 42, 64, 21, 38, 83, 74, 98, 61, 67, 72, 80, 14, 45, 89, 52, 53}
  3. Zip((("$\text{" * A) * " }$"), A, {"\phantom{clockwise}", "clockwise", "counterclockwise"}) → selectDirection
  4. Zip((("$\text{" * A) * "}$"), A, {"\phantom{180}", "90^\circ ", "180^\circ", "270^\circ"}) → selectAngle
  5. Element(randomList2, Mod[countQuestion, Length[randomList2]] + 1) → randomNum2
  6. Element(randomList1, Mod[countQuestion, Length[randomList1]] + 1) → randomNum1
  7. Element({verticesCase1(indexCase1), verticesCase2(indexCase2), verticesCase3(indexCase3)}, caseNum) → currentVertices
  8. Flatten(Sequence[Sequence[(i, j), i, -10, 10], j, -10, 10]) → gridPoints
  9. ClosestPoint(gridPoints, TriangleCenter[currentVertices(1), currentVertices(2), currentVertices(3), 1]) → CenterCase2
  10. Element({(0, 0), CenterCase2, centersCase3(indexCase3)}, caseNum) → RotationPoint
  11. Zip(Distance[RotationPoint, A], A, currentVertices) → distanceToCenter
  12. IndexOf(Max[distanceToCenter], distanceToCenter) → whichIndex
  13. 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
  14. Corner(5) → layoutAppSize
  15. Polygon({(-10.5, -10.5), (-10.5, 10.5), (10.5, 10.5), (10.5, -10.5)}) → viewbox
  16. Zip(Vector[UnitVector[Vector[CenterCase2, A]]], A, currentVertices) → vLabels
  17. Polygon(currentVertices) → triABC
  18. Rotate(triABC, (slideRotate * rotateAngle°), RotationPoint) → rotationTriangle
  19. Sequence(Vertex[rotationTriangle, A], A, 1, 3) → rotatedVertices
  20. Zip(Vector[Rotate[A, rotateDegrees°, RotationPoint]], Vector[A], vLabels) → vLabelsRotated
  21. Angle(currentVertices(whichIndex), RotationPoint, rotatedVertices(whichIndex)) → showAngleCounterClockwise
  22. Angle(rotatedVertices(whichIndex), RotationPoint, currentVertices(whichIndex)) → showAngleClockwise
  23. Textfield(StudentCenter) → inputCenter
  24. Zip(Text[("" * A), B + C, false, true, 0, 0], A, {"A", "B", "C"}, B, currentVertices, Vector[C], vLabels) → labelsABC
  25. Segment(rotatedVertices(whichIndex) + vArrow, rotatedVertices(whichIndex) + (0.2 * vArrow)) → directionArrow
  26. CircleArc(RotationPoint, If[¬clockwiseDirection, currentVertices(whichIndex), rotatedVertices(whichIndex) + (0.5 * vArrow)], If[¬clockwiseDirection, rotatedVertices(whichIndex), currentVertices(whichIndex) + (0.5 * vArrow)]) → displayRotation
  27. Zip(Text[("" * If[B ≠ D, A, ""]), B + C, false, true, 0, 0], A, {"A^{\prime}", "B^{\prime}", "C^{\prime}"}, B, rotatedVertices, Vector[C], vLabelsRotated, D, currentVertices) → labelsABCPrime
  28. Segment((-10.5, 0), (10.5, 0)) → axisSegmentX
  29. Segment((0, -10.5), (0, 10.5)) → axisSegmentY
  30. Text("x", (11.3, 0), true, true, 0, 0) → lblX
  31. Text("y", (0, 11.5), true, true, 0, 0) → lblY
  32. If(correctDirection, check, cross) → feedbackDirection
  33. If(correctAngle, check, cross) → feedbackAngle
  34. If(correctCenter, check, cross) → feedbackPoint

AI Drawing Prompt Reference

Draw a figure with two triangles. The left triangle is rotated to form the right triangle. The rotation center is located in the left-center of the figure. Arrows and labels connect the two triangles, indicating the rotation direction and angle. The figure also includes coordinate axes and grid lines to help locate the rotation center and angle. The overall layout is clear for demonstrating triangle rotation.
The prompt above was compiled from the original drawing commands and is for reference only.