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Midpoint Definition

Midpoint Definition
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2020-08-03 14:45
Coordinate GeometryTransformationGeometric Construction
This example illustrates the definition of the midpoint of a line segment. Key mathematical concepts include the midpoint, coordinates, and multiplication. Using GeoGebra commands such as Segment, Midpoint, Circle, etc., the midpoint of a line segment can be constructed and its properties observed. Suitable for students in middle school and above to learn basic concepts in coordinate geometry.

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)) * π), (-π)], M) → A'_1
  10. Rotate(A', If[2 < a ≤ 3, ((a - 2) * π), π], M) → A''
  11. Segment(A'_1, A'') → h'

AI Drawing Prompt Reference

Draw a line segment and find its midpoint. Use the midpoint as the center to draw a circle with a radius that is one-tenth of the line segment's length. Find the second intersection point of the circle with the line segment. Draw line segments from both ends of the original line segment to this intersection point. Then, perform scaling and translation operations on both ends of the line segment based on the midpoint. Finally, rotate both ends of the line segment by certain angles to create two new line segments.
The prompt above was compiled from the original drawing commands and is for reference only.