1. Pythagorean Theorem

2. a2 + b2 = c2

3. a2 + b2 = c2
= c2
= c2 5
106 = c2 9
106 = c
10.3 = c

4. a2 + b2 = c2
= c2
= c2 8
233 = c2 13
233 = c
15.3 = c

5. a2 + b2 = c2
72 + b2 = 102 10
49 + b2 = 100 7
b2 = 51
b = 51
b = 7.1

6. Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the eastbound car has traveled 8 miles. If the two cars are now a straight-line distance of 15 miles apart, how far has the northbound car traveled, to the nearest mile?
a2 + b2 = c2
82 + b2 = 152 15
64 + b2 = 225
b2 = 161 8
b = 161
b = 12.7

7. To get across a rectangular park that is 6 miles wide and 9 miles long, you can walk diagonally from corner to corner. How many miles do you save if you walk this way as opposed to walking around the park? 6
117 = c2 9
117 = c
a2 + b2 = c2
c = 10.9
= c2
= 4.1
= c2

8. Distance Formula

9. d = (x2 - x1)2 + (y2 – y1)2

10. What is the distance from (6,10) to (13,14)?
x1, y1
x2, y2
(x2 - x1)2 + (y2 – y1)2 = d
(13 - 6)2 + (14 – 10)2 = d
(7)2 + (4)2 = d
= d
65 = d
8.1 = d

11. What is the distance from (-2,5) to (-6,-1)?
x1, y1
x2, y2
(x2 - x1)2 + (y2 – y1)2 = d
(-6 – -2)2 + (-1 – 5)2 = d
(-4)2 + (-6)2 = d
= d
52 = d
7.2 = d

12. What is the distance from (-1,-4) to (-8,0)?
x1, y1
x2, y2
(x2 - x1)2 + (y2 – y1)2 = d
(-8 – -1)2 + (0 – -4)2 = d
(-7)2 + (4)2 = d
= d
65 = d
8.1 = d