# From Here to There - Applications of the Distance Formula

Recommended for High School.

## Introduction

Many problems in applied mathematics involve finding the distance between points. If we know the coordinates of a pair of points (*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2}), it is easy to find the distance between them by using the distance formula, which is a restatement of the Pythagorean Theorem.

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.

### Option 1

### Option 2

### Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

## Standards Correlations

See all standards correlations for *Real-World Math with Vernier* »

*Real-World Math with Vernier*

*Real-World Math with Vernier*

See other experiments from the lab book.