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Fraction & Graduated Half-line

Fraction & Graduated Half-line
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2014-11-17 04:11
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates determining the x-coordinate of a point on a graduated half-line in fractional form. It involves core math concepts like fractions, similar triangles, and coordinate geometry. GeoGebra commands and objects used include Line, Point, Random, Sequence, Segment, OrthogonalLine, Circle, Intersect, Vector, Element, and Translate. Suitable for middle school and above, focusing on the integration of coordinate geometry and fractional operations.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → a_1
  2. Point(a_1) → B
  3. Random(2, m * n) → haz_2
  4. Sequence(A + (B - A) * i / (m * n), i, 0, m * n) → liste3
  5. Segment(A, B) → a
  6. OrthogonalLine(A, a) → c_1
  7. Circle(A, s) → d
  8. Intersect(d, c_1) → C, D
  9. Segment(C, D) → c
  10. Circle(A, t) → f
  11. Intersect(f, c_1) → E, F
  12. Segment(F, E) → b
  13. Vector(F, E) → w
  14. Vector(E, F) → z
  15. Sequence(Segment[Translate[F, Vector[u * i]], Translate[E, Vector[u * i]]], i, 0, n) → liste1
  16. Sequence(Sequence[Segment[Translate[C, Vector[u * i + v * j]], Translate[D, Vector[u * i + v * j]]], j, 1, m - 1], i, 0, n - 1) → liste2
  17. Element(liste3, haz + 1) → U
  18. Element(liste3, haz_2) → H
  19. Translate(z, H + 2.2 * w) → e

AI Drawing Prompt Reference

Draw a horizontal line and mark a point B on it. Then generate a random point haz_2 at a height of m*n above B. Create a sequence of points between A and B to form a list. Connect A and B to draw a line segment. Draw a perpendicular line from A, intersecting the horizontal line at C and D. Connect C and D. Draw a circle from A, intersecting the perpendicular line at E and F. Connect E and F. Draw vectors from F to E and from E to F. Create sequences of translated segments based on these vectors to form two lists. Select a point U and a point H from the list, then translate them to get point e. The overall figure illustrates concepts of coordinate geometry and fractional operations.
The prompt above was compiled from the original drawing commands and is for reference only.