Question

find the distance from the point (3, -1, 12) 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, \( x = 3 \), \( y=- 1 \), and \( z = 12 \).

Step2: Substitute the values into the formula

Substitute \( x = 3 \), \( y=-1 \), and \( z = 12 \) into the formula: \( d=\sqrt{3^{2}+(-1)^{2}+12^{2}} \).
First, calculate the squares: \( 3^{2}=9 \), \( (-1)^{2}=1 \), \( 12^{2}=144 \).
Then, sum the squares: \( 9 + 1+144=154 \).
So, \( d=\sqrt{154} \).

Step3: Calculate the square root

\( \sqrt{154}\approx12.41 \) (rounded to the nearest hundredth).

Answer:

\( 12.41 \)