Students will have fun using the Pythagorean Theorem to find the distance between two points plotted on a coordinate grid.

**Lesson Objective:** The lesson is aligned to the Common Core State Standards for Mathematics – 8.G.8 Geometry – Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

**Materials Required:** graph paper, calculator

## Lesson Procedure:

**1. **The location of the exit door is (7, 8). Plot the location on the coordinate grid below. Label the point, X.

**2. **Your location is (4, 6). Plot the location on the coordinate grid. Label the point, *P*.

**3. **On the coordinate grid, draw a right triangle using these points as two of the corners of the right triangle.

**4. **Label the horizontal line segment, *a*. Label the vertical line segment, *b*.

**5. **Find the length of side *a* of the right triangle by subtracting the *x*-coordinates of the two points, *x*_{2} – *x*_{1} = *a *

**6. **Find the length of side *b* of the right triangle by subtracting the *y*-coordinates of the two points*, y*_{2} – *y _{1}* =

*b*

**7. **Use the Pythagorean Theorem, a^{2} + b^{2} = c^{2}, to find the length of side *c* of the right triangle. The length of side *c* is the distance between your location and the location of the exit door. Calculate the length to the nearest tenth.

**Answer: **3.6

## Individual or Group Work:

This lesson should help students discover the relationship between the Distance Formula,

d = √((*x _{2}* –

*x*) + (

_{1}*y*–

_{2}*y*)) and the Pythagorean Theorem, a

_{1}^{2}+ b

^{2 }= c

^{2}. Have students complete the following work sheet for further practice.

**Which Trap Door is Closest to Jack? Worksheet**

After completing all the lessons in this series, you can assess your student’s knowledge using **this downloadable assessment**.

## This post is part of the series: Teaching the Pythagorean Theorem.

- Lesson 1: Explaining the Proof of the Pythagorean Theorem
- Lesson 2: Finding the Missing Lengths using the Pythagorean Theorem
- Lesson 3: Protecting the Castle using the Pythagorean Theorem
- Lesson 4: Hunting for Treasure using the Pythagorean Theorem
- Lesson 5: Playing a Video Game using the Pythagorean Theorem