Question

find the distance from the point (8, 6, 1) 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, \( x = 8 \), \( y = 6 \), and \( z = 1 \).

Step2: Substitute the values into the formula

Substitute \( x = 8 \), \( y = 6 \), \( z = 1 \) into the formula: \( d=\sqrt{8^{2}+6^{2}+1^{2}} \).
First, calculate the squares: \( 8^{2}=64 \), \( 6^{2}=36 \), \( 1^{2}=1 \).
Then, sum them up: \( 64 + 36+1=101 \).
So, \( d=\sqrt{101} \).

Step3: Calculate the square root

\( \sqrt{101}\approx10.05 \) (rounded to the nearest hundredth).

Answer:

\( 10.05 \)