# The Distance Formula

the distance formula
Using the Distance Formula
8-G.B.8

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Students are introduced to the Distance Formula, $$\mathtt{d = \sqrt{a^2 + b^2}}$$, as derived from the Pythagorean Theorem. In the lesson, a and b will be expanded to show that they are equal to |x1 – x2| and |y1 – y2|, respectively.

Students will determine distances on the coordinate plane, first using the complete right triangle, then using just the drawn distance. Students should use calculators throughout this lesson.

In the second module, students use what they have learned about the Distance Formula and apply it to determine the perimeters and areas of polygons such as triangles, parallelograms, and trapezoids on the coordinate plane. At the end, students see that the Distance Formula can be applied even when given only a set of ordered pairs for a polygon’s vertices.

Finally, students will solve some application and mathematical problems using the Distance Formula.

Module 1 Video

This video introduces students to the Distance Formula as derived from the Pythagorean Theorem. This is not the Distance Formula as you know it, but is kept in this form to show how it is a re-expression of the Pythagorean Theorem in another form.