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Triangle Area Exploration by John Ulbright

Triangle Area Exploration by John Ulbright
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2015-04-23 02:29
TriangleCoordinate GeometryGeometric Construction
This example demonstrates exploring the area of a triangle through geometric construction. Key math concepts include the formula for the area of a triangle and coordinate geometry. GeoGebra commands such as Point, Polygon, and Centroid are used in construction. Suitable for middle school and above students learning geometry and area calculation.

GeoGebra Commands & Parameters

  1. Point({(hzoommin + hzoommax) / 2, (vzoommin + vzoommax) / 2}) → middle
  2. Point({Random[1, 10], Random[0, 10]}) → oneA
  3. Point({Random[1, 10], Random[0, 10]}) → oneB
  4. Point({Random[1, 10], Random[0, 10]}) → oneC
  5. Point({Random[21, 30], Random[0, 10]}) → threeA
  6. Point({Random[21, 30], Random[0, 10]}) → threeB
  7. Point({Random[21, 30], Random[0, 10]}) → threeC
  8. Point({Random[11, 21], Random[0, 10]}) → twoA
  9. Point({Random[11, 21], Random[0, 10]}) → twoB
  10. Point({Random[11, 21], Random[0, 10]}) → twoC
  11. Polygon(oneA, oneB, oneC) → polyOne, onec, onea, oneb
  12. Polygon(twoA, twoB, twoC) → polyTwo, twoc, twoa, twob
  13. Polygon(threeA, threeB, threeC) → polyThree, threec, threea, threeb
  14. Centroid(polyOne) → oneMiddle
  15. Centroid(polyTwo) → twoMiddle
  16. Centroid(polyThree) → threeMiddle
  17. Polygon(D, E, F, G) → poly1, d, e, f, g
  18. Polygon(H, I, J, K) → poly2, h, i, j, k
  19. Polygon(L, M, N, O) → poly3, l, m, n, o
  20. Point({(x(E) * (1 - t)) + (x(oneMiddle) * t), (y(E) * (1 - t)) + (y(oneMiddle) * t)}) → moveA
  21. Point({(x(I) * (1 - t)) + (x(twoMiddle) * t), (y(I) * (1 - t)) + (y(twoMiddle) * t)}) → moveB
  22. Point({(x(M) * (1 - t)) + (x(threeMiddle) * t), (y(M) * (1 - t)) + (y(threeMiddle) * t)}) → moveC
  23. PointIn(polyTwo) → PointpolyTwo_1
  24. Perimeter(polyTwo) → a
  25. PointIn(polyTwo) → PointpolyTwo
  26. Distance(twoA, twoa) → distancetwoAtwoa

AI Drawing Prompt Reference

Draw three random triangles on a coordinate plane, positioned in left, middle, and right regions, each formed by three random points. Mark the centroid of each triangle and connect each centroid to one vertex of its triangle with a dashed line. Also draw three quadrilaterals, where one vertex of each moves along a straight line from a fixed point to the corresponding triangle's centroid, creating a dynamic effect. Place a random point inside the middle triangle, and display its perimeter and the distance from one vertex to the opposite side. The overall scene illustrates the relationship between triangle area and geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.