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Explore Perpendicular Lines

Explore Perpendicular Lines
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2019-03-07 21:34
Coordinate GeometryGeometric Construction
This example demonstrates how to investigate perpendicular lines using GeoGebra, covering concepts like line equations, slopes, Pythagorean theorem, and angle calculations. It utilizes commands such as Element, Polygon, PointIn, Line, OrthogonalLine, Slope, LaTeX, Text, and Angle. Suitable for high school students and teachers to understand the criteria and properties of perpendicular lines.

GeoGebra Commands & Parameters

  1. Element({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}, m) → actualM
  2. Polygon({(-11, -11), (-11, 11), (11, 11), (11, -11)}) → viewBox
  3. PointIn(viewBox) → A
  4. PointIn(viewBox) → B
  5. Line(A, baseLine) → line1
  6. OrthogonalLine(B, baseLine) → line2
  7. Slope(line1) → slope1
  8. LaTeX("\text{Tilt}") → tilt
  9. LaTeX("\textbf{Instructions: }Lines 1 and 2 are perpendicular. Move the points and tilt the\\lines to investigate how they are related.") → INSTRUCTIONS
  10. LaTeX("\textbf{Question: }How are perpendicular lines related?") → QUESTION
  11. Slope(line2) → slope2
  12. Text("\textbf{Line \(1\)}", A + (-3.5, 0.5), true, true) → line1Label
  13. Text("\textbf{Line \(2\)}", B + (-3.5, 0.5), true, true) → line2Label
  14. Slope(line2) → slope2multiplier2
  15. Slope(line2) → slope2multiplier3
  16. Slope(line2) → slope2multiplier4
  17. Slope(line2) → slope2multiplier5
  18. Angle(line1, line2) → α