Question

find the distance from the point (-4, 3, -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 \( d=\sqrt{x^{2}+y^{2}+z^{2}} \). Here, \( x = - 4 \), \( y = 3 \), and \( z=-2 \).

Step2: Substitute the values into the formula

First, calculate \( x^{2}\), \( y^{2}\), and \( z^{2} \):
\( x^{2}=(-4)^{2}=16 \), \( y^{2}=3^{2} = 9 \), \( z^{2}=(-2)^{2}=4 \)
Then, sum these values: \( 16 + 9+4=29 \)

Step3: Take the square root

Now, find the square root of 29: \( d=\sqrt{29}\approx5.39 \) (rounded to the nearest hundredth)

Answer:

\( 5.39 \)