Difference between revisions of "Lines and Axes"
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− | <noinclude>{{Manual Page|version= | + | <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. | + | 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/> | + | {{example|1= 2D <br/> |
− | * Type in <code>g: 3x + 4y = 2</code> to enter line g as a linear equation. | + | * Type in <code>g: 3x + 4y = 2</code> to enter line ''g'' as a linear equation. |
− | * | + | * 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 | + | * 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.}} |
+ | |||
+ | |||
+ | {{example|1= 3D <br/> | ||
+ | * You can enter a line in parametric form thus: | ||
+ | ** <code>g: X = (1, 6, 3) + λ (7, -4, 4)</code> ; or via | ||
+ | ** <code>g: Line[(1, 6, 3), Vector[(7, -4, 4)]]</code> | ||
+ | * You can enter a line as an intersection of 2 planes, by one of the following 3 equivalent input : | ||
+ | ** <code>IntersectPath[4x+7y=46,y+z=9]</code><br/> | ||
+ | ** <code>(4x + 7y = 46, y + z = 9)</code><br/> | ||
+ | ** <code>7y = 46 - 4x = 7(9 - z)</code><br/> | ||
+ | }} | ||
+ | |||
==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 viag: 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 2.2y(a)
the value 3.3z(a)
the value -4.4 (because GeoGebra save the line equation as2.2 x + 3.3 y - 4.4 = 0
.
More informations: Coefficients Command