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Geogebra Demo: Equation of a Perpendicular Bisector

Geogebra Demo: Equation of a Perpendicular Bisector
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2019-05-13 22:03
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to draw and calculate the perpendicular bisector of a line segment using GeoGebra, including finding the midpoint, calculating slopes, and deriving the line equation. Key mathematical concepts involve midpoints, perpendicularity, slope computation, and linear equations. The construction leverages commands like Polygon, Length, Sequence, Element, UnitVector, Point, Zip, TableText, LineBisector, LaTeX, Segment, and Vector. Suitable for high school coordinate geometry education to enhance understanding of perpendicular bisectors' properties and applications.

GeoGebra Commands & Parameters

  1. Polygon({DataListFrameAnchor, DataListFrameAnchor + (12 * u), DataListFrameAnchor + (12 * u) - vHeight, DataListFrameAnchor - vHeight}) → ValueFrameTemplate
  2. Length(dTypes) → numSteps
  3. Sequence((-10, -20) + ((3.5 * i) * u), i, 0, 9) → iconAnchors
  4. Sequence(Translate[ValueFrameTemplate, Vector[(-((vHeight * i)))]], i, 0, numSteps - 1) → ValueFrames
  5. Sequence(Polygon[Element[iconAnchors, i], Element[iconAnchors, i + 1], 4], i, 1, (2 * Length[iconAnchors]), 2) → iconFrames
  6. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
  7. Element(G3, caseNum) → A3
  8. Element(G4, caseNum) → A4
  9. Polygon({ToolAnchor - (2 * v) - u, ToolAnchor + (4.5 * v) - u, ToolAnchor + (4.5 * v) + (26 * u), ToolAnchor - (2 * v) + (26 * u)}) → toolBar
  10. UnitVector(Vector[A3, A4]) → uAB
  11. Element(iconFrames, currentAction) → iconHighlighter
  12. Point(studentAnswer) → lblStudentLine
  13. Element(ValueFrames, 1) → vFrame1
  14. Element(ValueFrames, 2) → vFrame2
  15. Element(ValueFrames, 3) → vFrame3
  16. Element(ValueFrames, 4) → vFrame4
  17. Element(ValueFrames, 5) → vFrame5
  18. Element(ValueFrames, 6) → vFrame6
  19. Element(ValueFrames, 7) → vFrame7
  20. Zip(Element[ValueFrames, A], A, selectedList) → highlightedItems
  21. TableText({dDisplay}, "vc") → valueTbl
  22. TableText({Join[{{"\phantom{find the equation of a line through (-1,-3) with slope -5}"}, dSteps}]}, "vr") → stepsTable
  23. LineBisector(A3, A4) → answerLine
  24. LaTeX((((("\text{\textbf{Question: }" * QUESTION) * "\\\textbf{Instructions: }") * INSTRUCTIONS) * "}")) → allInstruc
  25. Segment(A3, A4) → D3
  26. LineBisector(A3, A4) → questionLine
  27. Vector((1, Slope[answerLine])) → test
  28. UnitVector(Vector[(1, Slope[answerLine])]) → uAnswer
  29. Segment((-10, 12), (-7, 12)) → legendLineK