Use the Pythagorean Theorem to hunt for buried treasure! Students will find the distance between two points plotted on a coordinate grid.

- slide 1 of 3
You are hunting for the hidden treasure. On the coordinate grid below, X marks the spot for the location of the treasure. Find the distance between your location and the location of the treasure.

**Learning 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 - slide 2 of 3
### Lesson Procedure

**1.**Your location is (6, 9). Plot the location on the coordinate grid below. Label the point,*P*.**2.**The location of the treasure is (3, 5). Plot the location on the coordinate grid. Label the point,*X*.**3.**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 treasure. Calculate the length to the nearest tenth.**Answer:**5 - slide 3 of 3
### Individual or Group Work

Provide the following worksheet to your students that sends them on a treasure hunt. Students will determine which treasure hunter is closest to the treasure by using the Distance Formula, d = √((

*x*_{2}-*x*_{1)}+ (*y*_{2}-*y*_{1}) ) and the Pythagorean Theorem, a^{2}+ b^{2}= c^{2}.

#### 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