Question

find the distance from the point (5, -1, -15) 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 $(5,-1,-15)$.

Step2: Substitute values

Substitute $x_1 = 0,y_1 = 0,z_1 = 0,x_2 = 5,y_2=-1,z_2=-15$ into the formula: $d=\sqrt{(5 - 0)^2+(-1 - 0)^2+(-15 - 0)^2}=\sqrt{5^2+( - 1)^2+( - 15)^2}$.

Step3: Calculate squares

Calculate the squares: $5^2=25$, $(-1)^2 = 1$, $(-15)^2=225$. Then $d=\sqrt{25 + 1+225}=\sqrt{251}$.

Step4: Approximate the value

$\sqrt{251}\approx15.84$.

Answer:

$15.84$