Question

find the distance from the point (-8, 4, 11) to the origin. write your answer as a whole number or as a decimal rounded to the nearest hundredth.

Explanation:

Step1: Recall the 3D distance formula

The distance \( d \) between a point \( (x, y, z) \) and the origin \( (0, 0, 0) \) is given by \( d=\sqrt{x^{2}+y^{2}+z^{2}} \). For the point \( (-8, 4, 11) \), we have \( x = - 8 \), \( y = 4 \), and \( z = 11 \).

Step2: Substitute the values into the formula

First, calculate the squares of each coordinate:
\( x^{2}=(-8)^{2}=64 \), \( y^{2}=4^{2} = 16 \), \( z^{2}=11^{2}=121 \).

Then, sum these squares: \( 64 + 16+121=201 \).

Step3: Take the square root

Now, find the square root of 201: \( d=\sqrt{201}\approx14.18 \) (rounded to the nearest hundredth).

Answer:

\( 14.18 \)