# Lesson 4: Hunting for Treasure using the Pythagorean Theorem

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

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}.