Lines and Axes

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Lines

You can enter a line as a linear equation in x and y or in parametric form into the Input Bar. In both cases previously defined variables (e.g. numbers, points, vectors) can be used within the equation.

Note: You can enter a line’s name at the beginning of the input followed by a colon.
Example: 2D
  • Type in g: 3x + 4y = 2 to enter line g as a linear equation.
  • You can enter a line in parametric form thus: g: X = (-5, 5) + t (4, -3)
  • Define the parameters m = 2 and b = -1. Then, you can enter the equation h: y = m*x + b to get a line h in y-intercept-form.


Example: 3D
  • You can enter a line in parametric form thus:
    • g: X = (1, 6, 3) + λ (7, -4, 4) ; or via
    • g: Line[(1, 6, 3), Vector[(7, -4, 4)]]
  • You can enter a line as an intersection of 2 planes, by one of the following 3 equivalent input :
    • IntersectPath[4x+7y=46,y+z=9]
    • (4x + 7y = 46, y + z = 9)
    • 7y = 46 - 4x = 7(9 - z)


Axes

The two coordinate axes are available in commands using the names xAxis and yAxis.

Example: The command PerpendicularLine[A, xAxis] constructs the perpendicular line to the x-axis through a given point A.

Comments

Get parameters of a line[edit]

From the line a: 2.2 x + 3.3 y = 4.4 you'll get with

  • x(a) the value 2.2
  • y(a) the value 3.3
  • z(a) the value -4.4 (because GeoGebra save the line equation as 2.2 x + 3.3 y - 4.4 = 0.

More informations: Coefficients Command

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