What is the distance between #(3,9,8)# and #(5,8,8)#?

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Answer 1 · 2018-05-12T02:50:56

#color(red)("distance" = sqrt5)# or #color(red)(~~2.236)# (rounded to thousandth's place)

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((5-3)^2 + (8-9)^2 + (8-8)^2)#

And now simplify:
#quadd = sqrt((2)^2 + (-1)^2 + (0)^2)#

#quadd = sqrt(4+1)#

#quadcolor(red)(d = sqrt5)# or #color(red)(~~2.236)# (rounded to thousandth's place)

Hope this helps!