What is the distance between #(6, 8, 2) # and # (4, 3, 1)
#?

Question

What is the distance between #(6, 8, 2)  # and # (4, 3, 1)
  #?

Julia Adams · Accepted Answer

undefined The distance between (6, 8, 2) and (4, 3, 1) is approximately 5.39 units.

Eva Abramson · Answer

I assume that you know the distance formula (square root of sum of corresponding coordinates squared)
Well, that formula can actually be EXTENDED to the third dimension. (This is a very powerful thing in future mathematics)
What that means is that instead of the known  #sqrt((a-b)^2 + (c-d)^2# We can extend this to be 
#sqrt((a-b)^2 + (c-d)^2 + (e-f)^2# This problem is beginning to look a lot easier huh?
We can just plug in the corresponding values into the formula #sqrt((6-4)^2 + (8-3)^2 + (2-1)^2# #sqrt(2^2 + 5^2 + 1^2)# This becomes #sqrt(4 + 25 + 1)# Which is #sqrt(30)# This cannot be simplified further, so we are done.

Kennedy Adams · Answer

undefined The distance between the points (6, 8, 2) and (4, 3, 1) in three-dimensional space can be calculated using the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

Substituting the coordinates of the points into the formula:

Distance = √((4 - 6)^2 + (3 - 8)^2 + (1 - 2)^2)
Distance = √((-2)^2 + (-5)^2 + (-1)^2)
Distance = √(4 + 25 + 1)
Distance = √30

So, the distance between the two points is √30 units.

What is the distance between #(6, 8, 2) # and # (4, 3, 1) #?