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LR7-01-XT1 (Midpoint of a line segment)

LR7-01-XT1 (Midpoint of a line segment)
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2019-05-09 01:41
Coordinate GeometryGeometric ConstructionSlider Animation
This interactive GeoGebra example demonstrates how the midpoint of a line segment is determined, visually showing that the midpoint divides the segment into two equal halves. The core mathematical concepts include line segments, midpoints, length measurement, and coordinate representation. In terms of construction, the example uses GeoGebra commands such as Polygon, Segment, Midpoint, Length, Point, Angle, Rotate, Line, and Vector, along with multiple sliders (e.g., sliderDrawFirstHalfSegment, sliderDrawSecondHalfSegment, sliderXFirstHalf) to control the display of segment halves and dynamic movement. LaTeX text and coordinate points (xCoordinate, yCoordinate) are also used to support explanations. This resource is suitable for middle or high school students learning plane geometry and coordinate geometry, and can be used for classroom demonstrations or self-directed exploration to understand the midpoint formula and its application in the coordinate plane.

GeoGebra Commands & Parameters

  1. Polygon({(-6, -1), (-3, -1), (-3, -9), (-6, -9)}) → pointABox
  2. Polygon({(7, 10), (3, 10), (3, 1), (7, 1)}) → pointBBox
  3. Polygon({(-11, -11), (-11, 11), (11, 11), (11, -11)}) → viewBox
  4. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  5. PointIn(pointABox) → A
  6. PointIn(pointBBox) → B
  7. Segment(A, B) → segment
  8. Midpoint(segment) → midpoint
  9. Length(Segment[A, midpoint]) → lengthOfHalfSegment
  10. Point(Circle[A, sliderDrawFirstHalfSegment]) → C
  11. Angle(C, A, midpoint) → α
  12. Rotate(Segment[A, Point[Circle[A, sliderDrawFirstHalfSegment]]], α, A) → firstHalfSegment
  13. Rotate(firstHalfSegment, sliderDrawSecondHalfSegment°, midpoint) → secondHalfSegment
  14. Line(A, x = 0) → xLineA
  15. Line(B, x = 0) → xLineB
  16. Segment(D, E) → segmentX
  17. Midpoint(segmentX) → midpointX
  18. Length(Segment[D, midpointX]) → lengthOfHalfX
  19. Point(Circle[D, sliderXFirstHalf]) → F
  20. Segment(D, F) → firstHalfX
  21. Rotate(D, sliderXSecondHalf°, midpointX) → D'
  22. Rotate(F, sliderXSecondHalf°, midpointX) → F'
  23. Segment(D', F') → secondHalfX
  24. Vector(D + (0, (-sliderXMove)), D + (0, (-sliderXMove)) + (sliderXArrows, 0)) → x1Vector
  25. Vector(E + (0, (-sliderXMove)), E + (0, (-sliderXMove)) + ((-sliderXArrows), 0)) → x2Vector
  26. LaTeX("\text{\(x\)-coordinate}") → xLabel
  27. LaTeX("\text{\(y\)-coordinate}") → yLabel
  28. Line(A, y = 0) → yLineA
  29. Line(B, y = 0) → yLineB
  30. LaTeX(("x=" * x(A))) → xLineALabel
  31. LaTeX(("\vphantom{-}x=" * x(B))) → xLineBLabel
  32. LaTeX(("y=" * y(A))) → yLineALabel
  33. LaTeX(("y=" * y(B))) → yLineBLabel
  34. Segment(G, H) → segmentY
  35. Point(Circle[G, sliderYFirstHalf]) → I
  36. Midpoint(segmentY) → midpointY
  37. Length(Segment[G, midpointY]) → lengthOfHalfY
  38. Rotate(Segment[G, Point[Circle[G, sliderYFirstHalf]]], 90°, G) → firstHalfY
  39. Rotate(firstHalfY, sliderYSecondHalf°, midpointY) → secondHalfY
  40. LaTeX((((("\text{The \(y\)-coordinate of the midpoint is halfway between the lines \(" * yLineALabel) * "\) and \(") * yLineBLabel) * "\).}")) → ySummary
  41. LaTeX((((("\text{The \(x\)-coordinate of the midpoint is halfway between the lines \(" * xLineALabel) * "\) and \(") * xLineBLabel) * "\).}")) → xSummary
  42. Vector(G + ((-sliderYMove), 0), G + ((-sliderYMove), 0) + (0, sliderYArrows)) → y1Vector
  43. Vector(H + ((-sliderYMove), 0), H + ((-sliderYMove), 0) + (0, (-sliderYArrows))) → y2Vector
  44. LaTeX(("A" * A)) → aLabel
  45. LaTeX(("B" * B)) → bLabel