The Cartesian plane distance formula determines the distance between two coordinates. You'll use the following formula to determine the distance (d), or length of the line segment, between the given coordinates.

d=√((x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2})

## How the Distance Formula Works

Consider a line segment identified by using the coordinates on a Cartesian plane.

To determine the distance between the two coordinates, consider this segment as a segment of a triangle. The distance formula can be obtained by creating a triangle and using the Pythagorean Theorem to find the length of the hypotenuse. The hypotenuse of the triangle will be the distance between the two points.

## Making a Triangle

To clarify, the coordinates x_{2} and x_{1} form one side of the triangle; y_{2} and y_{1} compose the third side of the triangle. Thus, the segment to be measured forms the hypotenuse and we are able to calculate this distance.

The subscripts refer to the first and second points; it doesn't matter which points you call first or second:

- x
_{2}and y_{2}are the x,y coordinates for one point - x
_{1}and y_{1}are the x,y coordinates for the second point - d is the distance between the two points