1. Finding the distance between two points. (-4,4) (4,-6)

2. Finding the distance between two points. Draw the right triangle as shown. (-4,4) (4,-6)(-4,-6) 4-(-6)=10

3. Find the length of each leg. (-4,4) (4,-6) (-4,-6) 10 4-(-4)=8

4. Using the Pythagorean theorem, 10 2 + 8 2 = D 2, we calculate the distance between the two points. 100+64 = 164 = D 2. Thus D = 164 (-4,4) (4,-6) (-4,-6) 10 4-(-4)=8

5. To find a formula for this problem, we will create the problem using variables. (x 1,y 1 ) (x 2,y 2 )

6. To find a formula for this problem, we will create the problem using variables. (x 1,y 1 ) (x 2,y 2 ) (x 2,y 1 ) x1x1 x2x2 x 2 - x 1 D

7. To find a formula for this problem, we will create the problem using variables. (x 1,y 1 ) (x 2,y 2 ) (x 2,y 1 ) x1x1 x2x2 y1y1 y2y2 x 2 - x 1 y 2 - y 1 D 2 = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 D

8. D = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 The distance formula is: Find the distance between (-2,8) and (9, -5) D = (9 - (-2)) 2 + (-5 - 8) 2

9. D = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 The distance formula is: Find the distance between (-2,8) and (9, -5) D = (9 - (-2)) 2 + (-5 - 8) 2 D = 11 2 + (-13) 2

10. D = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 The distance formula is: Find the distance between (-2,8) and (9, -5) D = (9 - (-2)) 2 + (-5 - 8) 2 D = 11 2 + (-13) 2 D = 121 + 169

11. D = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 The distance formula is: Find the distance between (-2,8) and (9, -5) D = (9 - (-2)) 2 + (-5 - 8) 2 D = 11 2 + (-13) 2 D = 121 + 169 D = 290