We will be closed on August 21 to allow our employees to enjoy the Great American Eclipse.

Vernier Software and Technology
Vernier Software & Technology

From Here to There - Applications of the Distance Formula

Figure from experiment 13 from Real-World Math with Vernier

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.

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 »

Activity 13 from Real-World Math with Vernier Lab Book

<i>Real-World Math with Vernier</i> book cover

Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.

Buy the Book

Go to top

We will be closed on August 21 to allow our employees to enjoy the Great American Eclipse.