# In this Section:

In this section, we learn how to find the distance between two points on a coordinate plane. We begin by learning about the
Pythagorean formula: a

^{2}+ b^{2}= c^{2}. This formula is a relationship between the sides of a right triangle. Using our Cartesian coordinate plane, we can connect any two points (x_{1},y_{1}),(x_{2},y_{2}) using a line. This line represents the hypotenuse of the right triangle or leg c. After this is completed, we can draw lines to represent legs a and b. These legs are the horizontal and vertical legs of the right triangle. We can measure the lengths of leg a along with leg b, and plug the results into the Pythagorean formula. This will allow us to solve for c (the hypotenuse) or distance between our two points. The distance formula is a direct application of this process. Instead of having to pullout a coordinate plane each time, we can simply label each point and plug into the formula. It relates c (the distance between the two points) to the square root of a^{2}+ b^{2}. a and b here represent the horizontal leg and vertical leg in the right triangle.