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Partitioning a Line Segment Level 2: Proportional Division and Midpoint Construc

Partitioning a Line Segment Level 2: Proportional Division and Midpoint Construc
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2018-08-25 09:54
Coordinate GeometryGeometric ConstructionSlider Animation
This GeoGebra example demonstrates how to partition a line segment into a given ratio, constructing the division point and related geometric relationships. The core mathematical concepts include the section formula for a line segment, midpoint, ratio and coordinate calculation, and equal-length division. Construction highlights: using GeoGebra commands Random, Segment, and Simplify; objects include points A, B, P, T, R, segments a, b, d, e, f, g, h, texts text1, text2, text3, button1, slider t, and variable r to control the partition ratio. Suitable for upper middle school or high school students to understand the section formula, coordinate geometry of proportional division, and interactive parameterized construction in dynamic geometry.

GeoGebra Commands & Parameters

  1. Random(-8, 6) → a
  2. Random(-3, 5) → b
  3. Random(-8, 6) → d
  4. Random(-3, 5) → e
  5. Segment(B, A) → f
  6. Segment(C, A) → g
  7. Segment(B, C) → h
  8. Segment(R, P) → i
  9. Segment(P, T) → j
  10. Simplify(a + (m * (d - a) / (m + n))) → t
  11. Simplify(b + (m * (e - b) / (m + n))) → r