Question

find the distance from the point (-8, -3, -7) to the origin. write your answer as a whole number or as a decimal rounded to the nearest hundredth.

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ in 3 - D space is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}$. The origin has coordinates $(0,0,0)$ and the given point is $(-8,-3,-7)$. So $x_1=-8,y_1 = - 3,z_1=-7,x_2 = 0,y_2 = 0,z_2 = 0$.

Step2: Substitute values

$d=\sqrt{(0-(-8))^2+(0 - (-3))^2+(0-(-7))^2}=\sqrt{(8)^2+(3)^2+(7)^2}$.

Step3: Calculate squares

$\sqrt{64 + 9+49}=\sqrt{122}$.

Step4: Find square - root and round

$\sqrt{122}\approx11.05$.

Answer:

$11.05$