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Interactive Definition Writing Prompt: Midpoint of a Segment

Interactive Definition Writing Prompt: Midpoint of a Segment
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2016-06-03 06:32
VectorCoordinate GeometryGeometric Construction
In collections Geometry: Introductory Definitions, Postulates, Theorems
This example demonstrates the interactive definition and properties of the midpoint of a segment. Key math concepts include line segments, midpoints, coordinate geometry, and geometric constructions. It utilizes GeoGebra commands such as Segment, Midpoint, Circle, Intersect, Dilate, and Rotate to construct the figure. Suitable for middle school students and above learning geometric constructions and coordinate geometry, as well as high school mathematics instruction.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Midpoint(f) → M
  3. Circle(M, (0.1 * f)) → c
  4. Intersect(c, f, 2) → D
  5. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], M) → A'
  6. Segment(A, A') → h
  7. Dilate(M, If[1 < a ≤ 2, 2 - a, 0], B) → C'
  8. Segment(M, C') → i
  9. Rotate(A, If[2 < a ≤ 3, ((-(a - 2)) * pi), (-pi)], M) → A'_1
  10. Rotate(A', If[2 < a ≤ 3, ((a - 2) * pi), pi], M) → A''
  11. Segment(A'_1, A'') → h'