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Midpoint and Length of a Line Segment

Midpoint and Length of a Line Segment
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2018-07-26 01:30
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the calculation of the midpoint and length of a line segment AB. It involves core mathematical concepts such as line segments, midpoints, lengths, and coordinate geometry. The construction uses commands like Segment, LineBisector, Intersect, OrthogonalLine, Angle, and Midpoint, along with objects like a, b, M, c, d, e, C, f, g, α, i, j, k, l, m, n, p, o, text1, h, D, E for labeling and computation. It is suitable for middle school and above students learning about line properties and applications of coordinate geometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. LineBisector(a) → b
  3. Intersect(a, b) → M
  4. OrthogonalLine(B, xAxis) → d
  5. OrthogonalLine(A, d) → e
  6. Intersect(e, d) → C
  7. Segment(B, C) → f
  8. Segment(A, C) → g
  9. Angle(B, C, A) → α
  10. Segment(A, B) → i
  11. Segment(B, C) → n
  12. Segment(C, A) → p
  13. Midpoint(g) → D
  14. Midpoint(f) → E

AI Drawing Prompt Reference

Draw a line segment AB, find its midpoint M. Then draw a line d perpendicular to AB, and a line e perpendicular to d. Find the intersection point C of lines e and d. Draw segments BC and AC. Calculate angle BAC and find the midpoint D of segment AC. Finally, mark the midpoint E.
The prompt above was compiled from the original drawing commands and is for reference only.