Question

find the distance from the point (8, -5, -2) 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 \( (8, - 5, - 2) \), we have \( x = 8 \), \( y=-5 \), \( z = - 2 \).

Step2: Substitute values into the formula

First, calculate \( x^{2}\), \( y^{2}\), and \( z^{2} \):
\( x^{2}=8^{2}=64 \), \( y^{2}=(-5)^{2}=25 \), \( z^{2}=(-2)^{2}=4 \).

Step3: Sum the squares

Sum these values: \( 64 + 25+4=93 \).

Step4: Take the square root

Now, find the square root of 93: \( d=\sqrt{93}\approx9.64 \) (rounded to the nearest hundredth).

Answer:

\( 9.64 \)