Difference between revisions of "Lines and Axes"

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<noinclude>{{Manual Page|version=4.0}}</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|geometric}}
{{objects|geometric}}
 
 
==Lines==
 
==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.
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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.}}
 
{{note|You can enter a line’s name at the beginning of the input followed by a colon.}}
  
{{example|1=<br/>
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{{example|1= 2D <br/>
* Type in <code>g: 3x + 4y = 2</code> to enter line g as a linear equation.
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* Type in <code>g: 3x + 4y = 2</code> to enter line ''g'' as a linear equation.
* Define a parameter t (e. g., t = 3) before entering line g in parametric form using<br><code>g: X = (-5, 5) + t (4, -3)</code>.
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* You can enter a line in parametric form thus: <code>g: X = (-5, 5) + t (4, -3)</code>
* Define the parameters m = 2 and b = -1. Then, you can enter the equation<br><code>h: y = m*x + b</code> to get a line h in y-intercept-form.}}
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* Define the parameters ''m'' = 2 and ''b'' = -1. Then, you can enter the equation <code>h: y = m*x + b</code> to get a line ''h'' in y-intercept-form.}}
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{{example|1= 3D <br/>
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* You can enter a line in parametric form thus:
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** <code>g: X = (1, 6, 3) + λ (7, -4, 4)</code> ; or via
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** <code>g: Line[(1, 6, 3), Vector[(7, -4, 4)]]</code>
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* You can enter a line as an intersection of 2 planes, by one of the following 3 equivalent input :
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** <code>IntersectPath[4x+7y=46,y+z=9]</code><br/>
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** <code>(4x + 7y = 46, y + z = 9)</code><br/>
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** <code>7y = 46 - 4x = 7(9 - z)</code><br/>
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}}
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==Axes==
 
==Axes==
 
The two coordinate axes are available in commands using the names ''xAxis'' and ''yAxis''.
 
The two coordinate axes are available in commands using the names ''xAxis'' and ''yAxis''.
 
{{example|1=The command <code>[[PerpendicularLine Command|PerpendicularLine]][A, xAxis]</code> constructs the perpendicular line to the x-axis through a given point A. }}
 
{{example|1=The command <code>[[PerpendicularLine Command|PerpendicularLine]][A, xAxis]</code> constructs the perpendicular line to the x-axis through a given point A. }}

Latest revision as of 08:11, 13 July 2017


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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