Question

find the distance from the point (13, 9, -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 \( (13, 9, - 2) \), we have \( x = 13 \), \( y=9 \), \( z=-2 \).

Step2: Substitute the values into the formula

First, calculate \( x^{2}+y^{2}+z^{2} \):
\( x^{2}=13^{2} = 169 \), \( y^{2}=9^{2}=81 \), \( z^{2}=(-2)^{2} = 4 \).
Then \( x^{2}+y^{2}+z^{2}=169 + 81+4=254 \).

Step3: Take the square root

Now, find the square root of 254: \( d=\sqrt{254}\approx15.94 \) (rounded to the nearest hundredth).

Answer:

15.94