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From Here to There - Applications of the Distance Formula

Figure from experiment 13 from Real-World Math with Vernier


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.


  • 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.

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