Chapter 11.1, Problem 4E

To determine

To complete:The statement “The distance between the points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ can be found using the _______ _______ in Space.”

Answer to Problem 4E

distance formula

Explanation of Solution

Given information:

The give statement is “The distance between the points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ can be found using the _______ _______ in Space.”

The distance between the two points can be calculated by the distance formula in space. Let’s there are two points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ are given in a three-dimensional coordinate system.

The distance formula to calculate the distance between the points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ is as follows.

  $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}$

Here, the distance between two points is $d$ .