Question

find the distance from the point (1, 5, 2) 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, \( x = 1 \), \( y = 5 \), and \( z = 2 \).

Step2: Substitute the values into the formula

Substitute \( x = 1 \), \( y = 5 \), \( z = 2 \) into the formula:
\( d=\sqrt{1^{2}+5^{2}+2^{2}}=\sqrt{1 + 25+4}=\sqrt{30} \)

Step3: Calculate the numerical value

\( \sqrt{30}\approx5.477225575\approx5.48 \) (rounded to the nearest hundredth)

Answer:

\( 5.48 \)