1. The Distance Formula with Ed and Leslie

2. Pythagorean Theorem Review Pythagorean Theorem: –Right Triangles: a 2 + b 2 = c 2 Pythagoras – 569 BC – 475 BC Pythagorean Brotherhood Motto: –“All is Number” Hippasus discovered irrational numbers c2c2 a2a2 b2b2 1 1

3. Horizontal Distance (2, 3)(11, 3) Hey Ed, How far apart are we? Not far enough. Just kidding. How should I know how far apart we are? Just count the spaces between us. Okay 123456 89 7 It looks like we are 9 spaces apart. That’s right! You could find that out by subtracting our x coordinates. That makes sense. Horizontal Distance is the change in the x direction.

4. Vertical Distance (5, 4) (5, 11) 1 2 3 4 5 6 7 7, The distance between us is 7. Ed, What is the distance between us now? Very Good, Ed. The vertical distance is the difference in the y coordinates. Let me count the spaces. Huh?

5. Hey, Ed come over Use the distance formula. How far is it? How should I know? What’s that? Distance Formula I can’t. It’s too far No it’s not Yes it is (2, 1) (8, 9) 10 Here it comes How do I use it? Great, I will be (x 2,y 2 ). Then we just use the formula. Here are my coordinates. Just use our coordinates in the formula. You can be (x 1,y 1 ). What are your coordinates?

6. Distance Formula (-4, 0) (4, 0) (0, -3)

7. Distance Formula & Pythagorean Theorem (x 1,y 1 ) (x 2,y 2 ) (x 2 -x 1 ) (y 2 -y 1 ) D = c = b = a

8. Mathematical Psychic Mind Reader