Last updated on September 25th, 2020

The distance formula is derived from the Pythagorean theorem. To find the distance between two points (X_{1}, Y_{1}) and (X_{2}, Y_{2}) all that you need to do is use the coordinates of these ordered pairs and apply the distance formula. Here is a step by step guide on how to find the distance between two coordinates.

The Distance Formula is:

x1 is the horizontal coordinate (along the x-axis) of Point 1, and x2 is the horizontal coordinate of Point 2. y1 is the vertical coordinate (along the y-axis) of Point 1, and y2 is the vertical coordinate of Point 2.

## Steps

- Take the
**coordinates of two points**you want to find the distance between.– For example, take the points (2,1) and (7,8). If (2,1) is (X

_{1}, Y_{1}), then (7,8) is (X_{2}, Y_{2}). **Find the horizontal and vertical distance**between the points.

– Find the distance along the x-axis. X_{2 }– X_{1}= 7 – 2 = 5.

– Find the distance along the y-axis. Y_{2 }– Y_{1 }= 8 – 1 = 7.**Square both axis**values.

– (X_{2 }– X_{1})² = 5² = 25

– (Y_{2 }– Y_{1})² = 7² = 49**Add the squared**values together.– (X_{2 }– X_{1})² + (Y_{2 }– Y_{1})² = 25 + 49 = 74- Take the
**square root****of the equation.**– √(X_{2 }– X_{1})² + (Y_{2 }– Y_{1}) = √74 ≈ 8.60

The distance between (2,1) and (7,8) is sqrt (74), or approximately 8.60 units.