Question

find the distance from the point (1, 7, -8) 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 space

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 \((0,0,0)\), and the given point is \((1,7,-8)\). So \(x_1 = 1,y_1=7,z_1=-8,x_2 = 0,y_2 = 0,z_2 = 0\).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step3: Calculate the square - root value

\(\sqrt{114}\approx10.68\)

Answer:

\(10.68\)