Question

find the distance from the point (9, -15, 4) 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 \( (9, - 15,4) \), we have \( x = 9 \), \( y=-15 \), and \( z = 4 \).

Step2: Substitute the values into the formula

First, calculate \( x^{2}\), \( y^{2}\), and \( z^{2} \):
\( x^{2}=9^{2}=81 \)
\( y^{2}=(-15)^{2}=225 \)
\( z^{2}=4^{2}=16 \)
Then, sum these values: \( 81 + 225+16=322 \)

Step3: Take the square root

Now, find the square root of 322: \( d=\sqrt{322}\approx17.94 \)

Answer:

\( 17.94 \)