Question

find the distance from the point (-8, 5, 4) 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 $(0,0,0)$ and the given point is $(-8,5,4)$. So $x_1=-8,y_1 = 5,z_1 = 4,x_2=0,y_2 = 0,z_2 = 0$.

Step2: Substitute values into formula

$d=\sqrt{(0 - (-8))^2+(0 - 5)^2+(0 - 4)^2}=\sqrt{(8)^2+(-5)^2+(-4)^2}=\sqrt{64 + 25+16}$.

Step3: Calculate the sum inside square - root

$64+25 + 16=105$. So $d=\sqrt{105}$.

Step4: Round the result

$\sqrt{105}\approx10.25$.

Answer:

$10.25$