Question

find the distance from the point (-1, 7, -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 $(0,0,0)$ and the given point is $(-1,7,-10)$. So $x_1=-1,y_1 = 7,z_1=-10,x_2 = 0,y_2 = 0,z_2 = 0$.

Step2: Substitute values into formula

$d=\sqrt{(0 - (-1))^2+(0 - 7)^2+(0-(-10))^2}=\sqrt{(1)^2+(-7)^2+(10)^2}$.

Step3: Calculate squares and sum

$d=\sqrt{1 + 49+100}=\sqrt{150}$.

Step4: Simplify and round

$\sqrt{150}\approx12.25$.

Answer:

$12.25$