# Lesson 11

Finding Distances in the Coordinate Plane

### Lesson Narrative

In this lesson, students continue to apply the Pythagorean Theorem to find distances between points in the coordinate plane.

Students who successfully answer the problems in the second activity use the structure of the coordinate plane to draw a right triangle, an example of looking for and making use of structure in the coordinate plane (MP7).

### Learning Goals

Teacher Facing

• Calculate the distance between two points in the coordinate plane by using the Pythagorean Theorem and explain (orally) the solution method.
• Generalize (orally) a method for calculating the length of a line segment in the coordinate plane using the Pythagorean Theorem.

### Student Facing

Let’s find distances in the coordinate plane.

### Student Facing

• I can find the distance between two points in the coordinate plane.
• I can find the length of a diagonal line segment in the coordinate plane.

Building Towards

### Glossary Entries

• Pythagorean Theorem

The Pythagorean Theorem describes the relationship between the side lengths of right triangles.

The diagram shows a right triangle with squares built on each side.  If we add the areas of the two small squares, we get the area of the larger square.

The square of the hypotenuse is equal to the sum of the squares of the legs. This is written as $$a^2+b^2=c^2$$.

• hypotenuse

The hypotenuse is the side of a right triangle that is opposite the right angle. It is the longest side of a right triangle.

Here are some right triangles. Each hypotenuse is labeled.

• legs

The legs of a right triangle are the sides that make the right angle.

Here are some right triangles. Each leg is labeled.