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

## 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

## 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}.

**Pythagorean Theorem Treasure Hunt Worksheet**

## 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