Question

find the distance from the point (-5, -7, -6) 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 \( (0, 0, 0) \) in 3 - D space is given by the formula \( d=\sqrt{x^{2}+y^{2}+z^{2}} \). For the point \( (-5,-7,-6) \), we have \( x = - 5 \), \( y=-7 \), and \( z = - 6 \).

Step2: Substitute the values into the formula

Substitute \( x=-5 \), \( y = - 7 \), and \( z=-6 \) into the formula:
\( d=\sqrt{(-5)^{2}+(-7)^{2}+(-6)^{2}} \)
First, calculate the squares of each number: \( (-5)^{2}=25 \), \( (-7)^{2} = 49 \), \( (-6)^{2}=36 \).
Then, add these values together: \( 25 + 49+36=110 \).
So, \( d=\sqrt{110} \).

Step3: Calculate the square root

\( \sqrt{110}\approx10.49 \) (rounded to the nearest hundredth).

Answer:

\( 10.49 \)