Question

find the distance from the point (1, 9, 5) 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 $(1,9,5)$.

Step2: Substitute values

Substitute $x_1 = 0,y_1 = 0,z_1 = 0,x_2 = 1,y_2 = 9,z_2 = 5$ into the formula: $d=\sqrt{(1 - 0)^2+(9 - 0)^2+(5 - 0)^2}=\sqrt{1 + 81+25}$.

Step3: Calculate the sum inside square - root

$1 + 81+25=107$. So $d=\sqrt{107}$.

Step4: Approximate the value

$\sqrt{107}\approx10.34$.

Answer:

$10.34$