What is the distance between #(–6, 3, 4) # and #(–5, –1, 1) #?

1 Answer
Dec 19, 2017

Answer:

#sqrt(26)#

Explanation:

You may be familiar with the two-dimensional distance formula, which tells us that the distance between #(x_1, y_1)# and #(x_2, y_2)# is:

#sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

There is a similar formula for three dimensions for the distance between #(x_1, y_1, z_1)# and #(x_2, y_2, z_2)#, namely:

#sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#

So in our example, the distance between #(x_1, y_1, z_1) = (-6, 3, 4)# and #(x_2, y_2, z_2) = (-5, -1, 1)# is:

#sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#

#= sqrt(((-5)-(-6))^2+((-1)-3)^2+(1-4)^2)#

#= sqrt(1^2+(-4)^2+(-3)^2)#

#= sqrt(1+16+9)#

#= sqrt(26)#