# Distance Between Two Points

- Author:
- Tamara Willis

## Learning Goal

Students will explore distance between two points in a coordinate plane and learn how this relates to right triangles.

## Visual 1: Click, drag, and drop the points to explore the distance between them.

## Question 1: Use the visual to...

Find the distance between each set of two points:

- (0,0) and (5,0)
- (0,0) and (0,5)
- (7,3) and (5,3)
- (-6,-4) and (-6,4)

## Question 1: Check your answer.

## Visual 2: Click, drag, and drop the points to explore the distance between them.

## Question 2: Use the visual to...

Find the distance between (1,1) and (8,6).

- What is different this time?
- Can this exact distance be found? Why or why not?

## Question 2: Check your answer.

## Attention: Did you notice the right triangle?

## Wherever there is a diagonal distance, there is also a right triangle.

- The
**longest side**of the right triangle (called the**hypotenuse**) is the diagonal distance. - The two
**shorter sides**of the right triangle (called the**legs**) make up the horizontal and vertical components of the diagonal distance.

## Visual 3: Click, drag, and drop the points and the lengths to estimate the distance.

## Question 3: Use the visual to...

Estimate the distance between each set of two points in terms of the lengths of the **hypotenuse** and **legs** of the right triangle:

- (0,0) and (6,3)
- (-3,5) and (2,1)
- (-7,-4) and (3,-8)
- (4,-2) and (0,2)

**hypotenuse**and

**leg**.