# Distance Between Two Points

## Learning Goal

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

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

Find the distance between each set of two points:

1. (0,0) and (5,0)
2. (0,0) and (0,5)
3. (7,3) and (5,3)
4. (-6,-4) and (-6,4)
Explain how you know.

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

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

1. What is different this time?
2. Can this exact distance be found? Why or why not?

## 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.
Click the most correct choice.

Select all that apply
• A
• B
• C
• D

## 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:

1. (0,0) and (6,3)
2. (-3,5) and (2,1)
3. (-7,-4) and (3,-8)
4. (4,-2) and (0,2)
What patterns are there between these lengths? Use the words hypotenuse and leg.