From Here to There - Applications of the Distance Formula > Experiment #14 from Real-World Math with Computers

Figure from experiment 14 from Real-World Math with Computers

Introduction

Many problems in applied mathematics involve finding the distance between points. If we know the coordinates of a pair of points (x₁, y₁) and (x₂, y₂) it is easy to find the distance between them by using the distance formula, which is a restatement of the Pythagorean Theorem.

$d = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}$

In this activity you will use a pair of Motion Detectors. They will record the Cartesian x, y coordinates of a rod moving in a star-shaped pattern. The data collected by the detectors will be used to test the distance formula.

Objectives

Record the x- and y-coordinates of a rod moving in a star pattern.
Use the recorded coordinates to calculate the distances moved between vertices of the star.
Compare the calculated distances with direct measurement on the star pattern.