Question

find the distance from the point (8, -6, -1) to the origin.
write your answer as a whole number or as a decimal rounded to the nearest hundredth.

Explanation:

Step1: Recall the distance formula in 3D

The distance \(d\) between two points \((x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}\). The origin is \((0,0,0)\), so \(x_1 = 0,y_1 = 0,z_1 = 0\) and \(x_2=8,y_2=-6,z_2 = - 1\).

Step2: Substitute values into the formula

$$
LATEXBLOCK0
$$

Step3: Calculate the value

\(\sqrt{101}\approx10.05\)

Answer:

\(10.05\)