1. M1A Warm Up: 1.Is there a way to rewrite a + b = c? Yes: a = c – b OR b = c - a 2.John visited three cities that lie on a coordinate grid at (-4, 5), (8, 5), (-4, -4). If he visited all three cities and ended up where he started, what is the distance in miles he traveled. 9 + 12 + 15 = 36 miles

2. Pythagorean Theorem and the Distance Formula Objective: Students will be able to: Explore the distance formula Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions.

3. Activity 1: Finding Distances

4. SchoolPost Office Fountain Fast Food Salon Grocery

5. (4,5) (-1,5) (-1,-7) (0,0) (3,0) (3,-4) School Post Office Fountain Fast Food Salon Grocery

6. Post Office School Fast Food Salon Grocery Fountain 5 12 13

7. Post Office School Fast Food Salon Grocery Fountain 3 5 4

8. Post Office School Fast Food Salon Grocery Fountain 3 5 4

9. Example 1: The distance from Jonestown to Maryville is 180 miles, the distance from Maryville to Elm City is 300 miles, and the distance from Elm City to Jonestown is 240 miles. Do the three towns form a right triangle? Explain.

10. Pythagorean Theorem: a a 2 + b 2 = c 2 WHAT DOES THIS MEAN??? Demo with Algebra Tiles! c b

11. Example 2: The irrational club wants to build a tree house. They have a 9 foot ladder that must be propped diagonally against the tree. If the base of the ladder is 5 feet from the bottom of the tree, how high will the tree house be off the ground?

12. If you only have two points, how do you find the distance between them? Find the distance between (-2, 4) and (-5, 6). Draw Manually!

13. Classwork: US Map Worksheet Kuta Software – The Distance Formula

14. Homework: Finish Kuta Software – The Distance Formula