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### Distance Formula

### 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. 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 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