Question

find the distance from the point (5, 7, 9) 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 \( d=\sqrt{x^{2}+y^{2}+z^{2}} \).

Step2: Substitute the values

For the point \( (5, 7, 9) \), we substitute \( x = 5 \), \( y = 7 \), and \( z = 9 \) into the formula:
\( d=\sqrt{5^{2}+7^{2}+9^{2}}=\sqrt{25 + 49+81} \)

Step3: Simplify the expression inside the square root

First, calculate the sum: \( 25+49 = 74 \), then \( 74 + 81=155 \). So, \( d=\sqrt{155} \)

Step4: Calculate the square root

\( \sqrt{155}\approx12.45 \) (rounded to the nearest hundredth)

Answer:

\( 12.45 \)