You can use GeoGebra
to draw curves using their parametrization:
If you need to find the parametrization of a line, see Item 4. When you find the parametrization, the line itself will also be drawn automatically.
If you want to draw curves in the plane, see Item 3.
If you want to draw curves in space, see Item 2.
GeoGebra
Instruction 1
3D Graphics
and Algebra View
under View
in Menu
. Algebra View
using the command Vector(<Point>)
for the command in the next steps to work. Note the name of the vector in Algebra View
, as you will need it later.
Algebra View
:
If you have a point and a direction vector, enter
Line(<Point>, <Direction Vector>)
and replace <Point>
with your point and <Direction Vector>
with the name of the vector from Step 2.
If you are given two points, enter
Line(<Point>, <Point>)
and replace both <Point>
fields with each of your points.
The line now appears in 3D Graphics
. You can also see the parametrization in Algebra View
.
Note! GeoGebra
uses the Greek letter for the parameter, instead of the usual .
3D Graphics
, click Rotate 3D Graphics view
. Example 1
Find the parametrization of the line through the point
with direction vector
Following Item 4 above, type
Line(<Point>, <Direction Vector>)
in its own line in Algebra View
. Then type
Line(<Point>, <Direction Vector>)
and replace <Point>
with (5, -6, 7)
and <Direction Vector>
with the name of the vector. You will then get the parametrization
Example 2
Find the parametrization of the line through the points
and
Following Item 4 above, type
Line(<Point>, <Point>)
and replace the first <Point>
field with (-3, 5, -4)
and the second <Point>
field with (-1, -1, -1)
. You will then get the parametrization
GeoGebra
Instruction 2
Algebra View
and Graphics View
under View
in Menu
. Curve(<Expression>, <Expression>, <Parameter Variable>, <Start Value>, <End Value>)
in Algebra View
. Make sure you use the version where there are two <Expression>
fields (there’s another one with three).
<Expression>
fields. Enter as <Parameter Variable>
, and set the start value and end value in the <Start Value>
and <End Value>
fields. Press Enter
. Your curve will appear in Graphics View
. Also, the parametrization will be printed in Algebra View
.
Example 3
Draw the curve with the parametrization
and
with 0 as start value and 50 as end value of parameter .
Following Item 3 above, use the command
Curve(<Expression>, <Expression>, <Parameter Variable>, <Start Value>, <End Value>)
by replacing
The first <Expression>
field with 3t
The second <Expression>
field with t+4
<Parameter Value>
with t
<Start Value>
with 0
<End Value>
with 50
The planar curve will appear in Graphics View
and parametrization in Algebra View
.
GeoGebra
Instruction 3
Algebra View
and 3D Graphics
under View
in Menu
. Curve(<Expression>, <Expression>, <Expression>, <Parameter-variable>, <Start>, <End>)
in Algebra View
. Make sure you use the one where there are three <Expression>
fields (there’s another one with three). Enter the expressions for , and , in that order, for <Expression>
. Enter as <Parameter Variable>
, and set the start and end values to for <Start>
and <End>
. Press Enter
.
Your curve will appear 3D Graphics
. Also, your parametrization is given in Algebra View
.
To change the perspective in 3D Graphics
, select the Rotate 3D Graphics view
tool and use the cursor to change the perspective to your liking.
Example 4
Draw the curve with the parametrization
and
with 0 as start value and 100 as end value of parameter .
Following Item 3 above, use the command
Curve(<Expression>, <Expression>, <Expression>, <Parameter Variable>, <Start Value>, <End Value>)
by replacing
The first <Expression>
field with t
The second <Expression>
field with -2t+1
The third <Expression>
field with t+2
<Parameter Value>
with t
<Start Value>
with 0
<End Value>
with 100
The spacial curve will appear in Graphics View
and parametrization in Algebra View
.