The Pythagorean theorem states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. The theorem can be expressed as a2 + b2 = c2, where a and b are the legs and c is the hypotenuse. The distance formula is used to calculate the distance between two points in a coordinate plane. It is calculated by taking the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates of the two points. For example, to find the distance between points (3,17) and (5,27), you would calculate √(5-3)2 +

1. “ Pythagorean Theorem and Distance Formula” Andre Goins

2. Pythagorean Theorem Pythagorean The Pythagorean Theorem says that in any right triangle, the lengths of the three sides are related ( a 2 +b 2 =c 2 ) The “a & b” stands for the legs of the triangle. The “c” is the Hypotenuse. The Pythagorean only applies to right triangles

3. Pythagorean Theorem Example a 2 +b 2 =c 2 34 2 +32 2= c 2 1156+1024=c C=2180 C=46.69 34 32 x

4. Distance Formula Distance formula is a method that is used to find the space between to points √ (x 2 -x 1 ) 2 +(y 2 -y 1 ) 2 You must first subtract the X-coordinates from each other and do the same for the y-coordinates Then you must multiply the difference of the coordinates by its self. Add the products together Square root the sum Round to the nearest tenth if needed

5. √ (x 2 -x 1 ) 2 +(y 2 -y 2 ) 2 √ (5-3) 2 +(27-17) 2 √ (2) 2 +(10) 2 √ 4+100 √ 104 10.20 (3,17) (5,27)