The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. The distance formula calculates the distance between two points by taking the square root of the sum of the squares of the differences between their x- and y-coordinates. An example shows using the distance formula to find the distance between points (4,9) and (16,3), which equals 12.94.

1. Pythagorean Theorem and Distance formula By Ladasha Johnson

2. Pythagorean Theorem Explanation Slide Pythagorean Theorem is a2 + b2= c2. The variables a and b stands for the legs of the triangle, and c stands for the hypotenuse. We always use a right triangle for the theorem.

3. Pythagorean Theorem Example Slide My right triangle. 8 6 x A 2 + b 2 = c 2 8 2 + 6 2 = c 2 64 + 36= 100 square root= 10

4. Distance Formula Distance formula is ( x 1 - x 2 ) ( y 1 - y 2 ). The steps that you follow to use the distance formula is label the points, (x 1 - y 1 ) (x 2 - y 2 ), and after that you do the math.

5. Distance Formula Example Slide (4,9) (16,3) 4= x 9= y 16=x 3=y 4-16= -12 2 9-5= 4 2 -12 2 = 144 4 2 = 16 144+16= 160 Square root 160=12.94