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Equations of Parallel and Perpendicular Lines

Equations of Parallel and Perpendicular Lines
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2019-01-09 10:50
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the relationship between equations of parallel and perpendicular lines. Key math concepts include equal slopes for parallel lines and product of slopes being -1 for perpendicular lines. Construction highlights the use of DynamicCoordinates, Line, OrthogonalLine, GCD, LCM, Midpoint, Slope, If, Angle, Segment commands and objects in GeoGebra. Suitable for high school students learning coordinate geometry.

GeoGebra Commands & Parameters

  1. DynamicCoordinates(C', (round(x(C') / 0.5) * 0.5), (round(y(C') / 0.5) * 0.5)) → P
  2. DynamicCoordinates(B', (round(x(B') / 0.5) * 0.5), (round(y(B') / 0.5) * 0.5)) → B
  3. DynamicCoordinates(A', (round(x(A') / 0.5) * 0.5), (round(y(A') / 0.5) * 0.5)) → A
  4. Line(B, A) → L_1
  5. OrthogonalLine(P, L_1) → L_3
  6. GCD({Numerator[x(L_3)], Numerator[y(L_3)], Numerator[z(L_3)]}) → hcf3
  7. LCM({Denominator[x(L_3)], Denominator[y(L_3)], Denominator[z(L_3)]}) → lcm3
  8. Line(P, L_1) → L_2
  9. Midpoint(A, B) → M
  10. Slope(L_3) → m_3
  11. If(m_3^(2) ≠ 1, FractionText[m_3], If[m_3 ≟ -1, "-", ""]) → textm3
  12. Angle(L_1, L_3) → α
  13. Slope(L_2) → m_2
  14. GCD({Numerator[x(L_2)], Numerator[y(L_2)], Numerator[z(L_2)]}) → hcf2
  15. LCM({Denominator[x(L_2)], Denominator[y(L_2)], Denominator[z(L_2)]}) → lcm2
  16. If(m_2^(2) ≠ 1, FractionText[m_2], If[m_2 ≟ -1, "-", ""]) → textm2
  17. Segment(M, A) → f
  18. Segment(M, B) → g
  19. GCD({Numerator[x(L_1)], Numerator[y(L_1)], Numerator[z(L_1)]}) → hcf1
  20. LCM({Denominator[x(L_1)], Denominator[y(L_1)], Denominator[z(L_1)]}) → lcm1
  21. Slope(L_1) → m_1