Question

find the distance from the point (7, 8, 6) 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 $(7,8,6)$.

Step2: Substitute values

Substitute $x_1 = 0,y_1 = 0,z_1 = 0,x_2 = 7,y_2 = 8,z_2 = 6$ into the formula: $d=\sqrt{(7 - 0)^2+(8 - 0)^2+(6 - 0)^2}=\sqrt{7^2+8^2+6^2}$.

Step3: Calculate squares

$7^2=49$, $8^2 = 64$, $6^2=36$. So $d=\sqrt{49 + 64+36}$.

Step4: Add values inside square - root

$49+64 + 36=149$. So $d=\sqrt{149}$.

Step5: Approximate value

$\sqrt{149}\approx12.206555$. Rounding to the nearest hundredth, $d\approx12.21$.

Answer:

$12.21$