# What is the distance between # (–2, 1, 3) # and #(8, 6, 0) #?

##### 2 Answers

#### Explanation:

First, calculate your distance per dimension:

#x : 8+2 = 10# #y : 6-1 = 5# #z : 3+-0 = 3#

Next, apply **3D Pythagoras' theorem**:

Where:

#h^2# is the square of the distance between two points#a^2# ,#b^2# , and#c^2# are the calculated dimensional distances

We can adjust the theorem to solve directly for

Finally, substitute your values into the equation and solve:

#### Explanation:

The distance formula for Cartesian coordinates is

Where

Let

Hence the distance between the given points is