What is the distance between #(4, –1, 2) # and #(4, –4, –2)#?

1 Answer
George C.
Apr 6, 2016

#5#

Explanation:

In general, the distance between points #(x_1, y_1, z_1)# and #(x_2, y_2, z_2)# is given by the distance formula:

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

In our particular example, we have #x_1 = x_2# and this simplifies to what is basically a #3,4,5# right angled triangle, but evaluating the formula directly we get:

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

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

#=sqrt(0^2+(-3)^2+(-4)^2)#

#=sqrt(0+9+16)#

#=sqrt(25)#

#=5#

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