Lesson objective: Find the distance between points.

This lesson helps to build procedural skill with calculating unknown lengths of right triangles and distance between points in two-dimensional space. Triangles and the coordinate plane are used here because both representations guide students to connect the Pythagorean Theorem with diagonal distance. This work develops students' understanding that we can use the relationships shown in the Pythagorean Theorem to solve problems given particular pieces of information about the problem.

Students engage in Mathematical Practice 8 (look for and express regularity in repeated reasoning) as they recognize that right triangle relationships can be used to find any diagonal length or distance.

**Key vocabulary:**

- coordinate plane
- diagonal
- distance
- horizontal
- Pythagorean Theorem
- vertical

**Special materials needed:**

- graph paper (not required, but helpful)