What is the distance between #(3,15,-2)# and #(-4,15,4)#?

1 Answer
Feb 16, 2016

Answer:

#sqrt(85) approx 9.2195#

Explanation:

Use the three-dimensional distance formula, which can be derived by applying the Pythagorean Theorem twice. Given two points in 3-dimensional space written in rectangular coordinates #(x_1,y_1,z_1)# and #(x_2,y_2,z_2)#, the distance is:

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

For the problem at hand, this becomes

#dist=sqrt(7^2+0^2+6^2)=sqrt(49+36)=sqrt(85) approx 9.2195#.