Education Technology

Equations for Curves Passing through a Given Set of Points

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