What is the distance between #(-4,-3,4)# and #(-30,15,-16)#?

1 Answer
May 31, 2018

Answer:

#quadcolor(red)(d = 10sqrt14)# or #color(red)(~~37.417)# (rounded to thousandth's place)

Explanation:

The distance between three dimensions is similar to the distance between two dimensions.

We use the formula:
#quadcolor(red)(d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2))#, where #x#, #y#, and #z# are the coordinates.

Let's plug in the values for the coordinates into the formula. Pay attention to the negative signs:
#quadd = sqrt((-30-(-4))^2 + (15-(-3))^2 + (-16-4)^2)#

And now simplify:
#quadd = sqrt((-26)^2 + (18)^2 + (-20)^2)#

#quadd = sqrt(676 + 324 + 400)#

#quadd = sqrt(1400)#

#quadd = sqrt(100 * 14)#

#quadd = sqrt100sqrt14#

#quadd = 10sqrt14#

#quadcolor(red)(d = 10sqrt14)# or #color(red)(~~37.417)# (rounded to thousandth's place)

Hope this helps!