Question

find the distance from the point (-13, -8, 10) 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 is the point $(0,0,0)$ and the given point is $(-13,-8,10)$. So $x_1=-13,y_1 = - 8,z_1=10,x_2 = 0,y_2=0,z_2 = 0$.

Step2: Substitute values into formula

$d=\sqrt{(0-(-13))^2+(0 - (-8))^2+(0 - 10)^2}=\sqrt{13^2+8^2+(- 10)^2}=\sqrt{169 + 64+100}$.

Step3: Calculate sum inside square - root

$169+64 + 100=333$.

Step4: Find square - root

$d=\sqrt{333}\approx18.25$.

Answer:

$18.25$