Pythagorean Theorem

a2 + b2 = c2

a2 + b2 = c2 52 + 92 = c2 25 + 81 = c2 5 106 = c2 9 106 = c 10.3 = c

a2 + b2 = c2 82 + 132 = c2 64 + 169 = c2 8 233 = c2 13 233 = c 15.3 = c

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

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

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 62 + 92 = c2 6 + 9 - 10.9 = 4.1 36 + 81 = c2

Distance Formula

d = (x2 - x1)2 + (y2 – y1)2

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 49 + 16 = d 65 = d 8.1 = d

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 16 + 36 = d 52 = d 7.2 = d

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 49 + 16 = d 65 = d 8.1 = d