6.1.3 Parameterizing a line segment
Parameterizing is the act of writing a set of parametric equations that describes a curve (in math we consider lines and line segments curves too).
One aspect of parameterizing that can be tricky is that there is not a single way to parameterize the same curve. In the GeoGebra applet below you can see three different parameterizations of the same line segment. Hit "Animate" to see the differences.
Parameterizing includes extra information that an expression relating and does not. This includes orientation (the arrow indicating the direction of movement as the parameter increases) and speed (think of this as a measure of the distance traveled from one point on the parametric curve to the next as the parameter increases).
To parameterize a line segment that travels from point to point over the domain , use the following parametric equations:
Use the GeoGebra applet below to practice parameterizing directed line segments (directed means there is a direction of movement - the orientation of the parameterized line segment). In this applet you can change the starting point and the ending point . The "Animate" button will draw the directed line segment from to . You can then type in what you think the parametric equations for this line segment are and check your work and click "show curve" to check your work. Now the Animate button will also draw your parameterized curve. If you have correctly parameterized the directed line segment your curve will show up in green. Otherwise your curve will show up in red.