Vernier Software & Technology

# From Here to There - Applications of the Distance Formula

## 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 the vertices of the star.
• Compare the calculated distances with direct measurement on the star pattern.

## Sensors and Equipment

This activity features the following Vernier sensors and equipment.