How accurate is the distance formula?

Vernier is a company that produces software and equipment to be used in education. For this specific lesson, motion detectors are used to gather data. Students have the opportunity to work in groups developing a model to determine the accuracy of the distance formula. By working in groups, students have the opportunity to practice standards in mathematics such as construct variable arguments and critique the reasoning of others and model with mathematics. The activity is also aligned with the CCSS.MATH.CONTENT.HSG.GPE.B.7
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.^*

In this activity, students use the distance formula to find the distance between two points. Using the motion detectors, students can create a “live” cartesian plane and determine the coordinates of 5 points.

Students have to find the distance not only with the distance formula but also with a meter/yard stick. They will be recording their data in a table (Figure 1).By making measurements with different tools, students have the opportunity’s to develop ideas that connect to the concept of distance between two points.  After the data is collected, students need to compare/contrast both measurements,  determine which one is more accurate and explain their reasoning .

Figure 1

Find more about this the activity here: from-here-to-there