Question

find the distance from the point (-6, -10, -8) 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 \( (-6, - 10, -8) \), we have \( x=-6 \), \( y = - 10 \), \( z=-8 \).

Step2: Substitute the values into the formula

First, calculate \( x^{2}\), \( y^{2}\), and \( z^{2} \):
\( x^{2}=(-6)^{2}=36 \)
\( y^{2}=(-10)^{2} = 100 \)
\( z^{2}=(-8)^{2}=64 \)
Then, sum these values: \( 36 + 100+64=200 \)

Step3: Take the square root

Now, find the square root of 200: \( d=\sqrt{200}\approx14.14 \) (rounded to the nearest hundredth)

Answer:

14.14