# Lesson 5: Playing a Video Game using the Pythagorean Theorem

Students will practice the Pythagorean Theorem through the scenario of playing a video game. Have your students find the distance between their location and the location of the exit door to the next level of the game.

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**.