1. Distance between two points
Unit 5 Lesson 1
Distance between two points

2. How do we find the distance between two points?
Suppose we are asked to find the distance between the points C(1, 3) and D(-2, 4). How would we begin to find the distance?

3. 1. Let’s graph the points on a coordinate plane so we can visualize the distance between these points

4. Notice how we created a right triangle.
2. Now let’s draw a path from one point to the next point in the shape of a triangle.
Notice how we created a right triangle.

5. 3. Since we now have a right triangle, we can use the Pythagorean theorem to find the distance between the points.
The Pythagorean Theorem:
a2 + b2 = c2
For our problem, a = 1, b = 3 and c is the unknown.
Substituting into the formula…
(1)2 + (3)2 = c2
1 + 9 = c2
10 = c2
= c 1 3

6. Distance Formula
Using the Pythagorean Theorem, we can create a formula that will allow us to find the distance between two points.
Using the points:

7. Our problem revisited using the distance formula….
Suppose we are asked to find the distance between the points C(1, 3) and D(-2, 4). Substituting into the distance formula….

8. Conclusions
We can use the Pythagorean Theorem to find distances between points.
We can also use the distance formula to find distances between points.