Question

find the distance from the point (5, 9, 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 $(5,9,4)$. So $x_1 = 0,y_1 = 0,z_1 = 0,x_2 = 5,y_2 = 9,z_2 = 4$.

Step2: Substitute values into formula

$d=\sqrt{(5 - 0)^2+(9 - 0)^2+(4 - 0)^2}=\sqrt{5^2+9^2+4^2}=\sqrt{25 + 81+16}$.

Step3: Calculate sum inside square - root

$25+81 + 16=122$. So $d=\sqrt{122}$.

Step4: Round the result

$\sqrt{122}\approx11.05$.

Answer:

$11.05$