Free Algebra
Tutorials!
 
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


The Distance Formula

Consider the points (x1, y1) and (x2, y2) as shown in the figure below.

The distance between these points is the length of the hypotenuse of a right triangle as shown in the figure. The length of side a is y2 - y1 and the length of side b is x2 -  x1. Using the Pythagorean theorem, we can write

d2 = (x2 -  x1)2 + (y2 - y1)2.

If we apply the even-root property and omit the negative square root (because the distance is positive), we can express this formula as follows.

 

Distance Formula

The distance d between (x1, y1) and (x2, y2) is given by the formula

 

Example

Using the distance formula

Find the length of the line segment with endpoints (-8, -10) and (6, -4).

Solution

Let (x1, y1) = (-8, -10) and (x2, y2) = (6, -4). Now substitute the appropriate values into the distance formula:

The exact length of the segment is .

 

 
All Right Reserved. Copyright 2005-2024