Activity Overview
In this Derive™ activity, students explore equations of curves which pass through a set of given points. They use this method to determine the location of a distribution center which is equidistant from the outlets of a large department store chain.
Before the Activity
See the attached DFW file for detailed instructions for this activity
Print pages from the attached DFW file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity Procedures:
Set up a 2D plot window
Use 3 random locations on the coordinate system
Simplify the expression and assign result to the variable loc
Guess the best location for the center of a circle which encompasses the 3 points
Substitute guesses for the center and radius of the circle in the equation for the center of a circle and plot the result
Expand the equation of the circle
Simplify the given expression to see the three unknown equations
Solve for the radius, and the coordinates of the center
Extend the procedure to find a curve that passes through a given number of points by considering the equation for a parabola
Generate three points at random and assign the result to a variable
Plot the three points
Substitute these three points into the equation of the parabola to obtain three equations in the three unknowns
Solve the equations for the unknowns and plot the parabola
After the Activity
Students answer questions listed on the activity sheet.
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary