Question

find the distance from the point (2, 4, 3) 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 \( (2, 4, 3) \), we substitute \( x = 2 \), \( y = 4 \), and \( z = 3 \) into the formula.

Step2: Calculate the sum of squares

First, calculate \( x^{2}+y^{2}+z^{2} \): \( 2^{2}+4^{2}+3^{2}=4 + 16+9=29 \).

Step3: Take the square root

Then, take the square root of 29: \( d=\sqrt{29}\approx5.39 \) (rounded to the nearest hundredth).

Answer:

\( 5.39 \)