Question

find the distance from the point (2, 2, 7) 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 the point $(0,0,0)$ and the given point is $(2,2,7)$.

Step2: Substitute values

Substitute $x_1 = 0,y_1 = 0,z_1 = 0,x_2 = 2,y_2 = 2,z_2 = 7$ into the formula: $d=\sqrt{(2 - 0)^2+(2 - 0)^2+(7 - 0)^2}=\sqrt{2^2+2^2+7^2}$.

Step3: Calculate squares

$2^2=4$, $2^2 = 4$, and $7^2=49$. So $d=\sqrt{4 + 4+49}=\sqrt{57}$.

Step4: Approximate the value

$\sqrt{57}\approx7.55$.

Answer:

$7.55$