# Activities

• • • ##### Subject Area

• Math: Geometry: Vectors

• ##### Author 9-12

45 Minutes

Derive™ 6

• ##### Report an Issue

Trying to Find a 'Best' Fit - A Heuristic Approach

#### Activity Overview

In this Derive™ activity, students determine the optimal location for a warehouse so that it is close to the center of a circle that passes through all the outlets of a store in the region.

#### 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.

• Set up a 2D plot window
• Place a coordinate system over the region and assign each store a point on the system
• Optimal location for the warehouse is close to the center of a circle that passes through the points representing each store
• Understand that if center is at (c1, c2) and has a radius, r, then each of the coordinates (x, y) for the store would satisfy the equation (x ? c1)2 + (y ? c2)2 = r2
• Use the circle equation, randomly generated seven points and find all equations
• Evaluate the weighted averages, the average equation representing a set result, and store the values in a vector
• Solve the set of equations for the radius, and the coordinates of the center
• Substitute the result values in the equation of the circle, and plot a graph
• Generate a best fitting curve
• #### 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