Distance between two points

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Presentation transcript:

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

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?

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

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.

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

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:

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….

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