Pythagorean Theorem and Distance Formula

By: Tristin Patton

Pythagorean Theorem

• The Pythagorean Theorem states that in any right triangle, the lengths of the three sides are related as follows: a 2 + b 2 = c 2   where c is the measure of the right triangle's hypotenuse (or longest side) and a and b are the measures of its two legs.

4

3??

32+42=???

9+16=25

The square root of 25 is 5.

=5

The Distance Formula• The formula that allows you to find the

distance between two points in the xy-plane. For example, the distance between points (x2, y2) and (x1, y1) is shown below.

(X2-X1)2 +(Y2-Y1)2

(2,4)

(7,13)

(7-2)2+(13-4)2

52+92

25+81=106

The square root of 106 is 10.3. The distance between (2,4) and (7,13) is 10.32.