Question

find the distance from the point (-1, 3, 19) 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 \( (-1, 3, 19) \), we have \( x = - 1 \), \( y=3 \), and \( z = 19 \).

Step2: Substitute the values into the formula

First, calculate the squares of each coordinate: \( (-1)^{2}=1 \), \( 3^{2} = 9 \), and \( 19^{2}=361 \). Then sum these squares: \( 1 + 9+361=371 \).

Step3: Take the square root

Now, find the square root of \( 371 \): \( d=\sqrt{371}\approx19.26 \) (rounded to the nearest hundredth).

Answer:

\( 19.26 \)