How to Find the Distance Between Two Coordinates

Last updated on September 25th, 2020

The distance formula is derived from the Pythagorean theorem. To find the distance between two points (X₁, Y₁) and (X₂, Y₂) 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

1. 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 (X₁, Y₁), then (7,8) is (X₂, Y₂).
   

2. Find the horizontal and vertical distance between the points.
   – Find the distance along the x-axis. X₂ – X₁= 7 – 2 = 5.
   – Find the distance along the y-axis. Y₂ – Y₁ = 8 – 1 = 7.
   
   
3. Square both axis values.
   – (X₂ – X₁)² = 5² = 25
   – (Y₂ – Y₁)² = 7² = 49
   
   
4. Add the squared values together.
   –  (X₂ – X₁)² + (Y₂ – Y₁)² = 25 + 49 = 74
   
   
5. Take the square root of the equation.
   – √(X₂ – X₁)² + (Y₂ – Y₁) = √74 ≈ 8.60

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