Question

1. what is the formula for calculating the distance between two points in three - dimensional space?

a. $(x_2 + x_1)+(y_2 + y_1)+(z_2 + z_1)$
b. $sqrt{(x_2 + x_1)^2+(y_2 + y_1)^2+(z_2 + z_1)^2}$
c. $sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}$
d. $(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2$

Explanation:

Step1: Recall distance formula concept

The distance $d$ between two points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ in 3 - D space is based on the Pythagorean theorem extension.
The formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}$.

Answer:

C. $\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}$