Question

The distance between the $x$-axis and the point $(3,12,5)$ is:

• A. $3$
• B. $13$
• C. $14$
• D. $12$
• E. $5$

Answer 1

The correct option is B

$13$

Explanation for the correct option:

Caculating the distance:

Given the two points $(3,12,5)$ and $x$-axis:

$$\begin{gathered} A\left(x_1,y_1,z_1\right)=\left(3,12,5\right) \\ \text{The point is on the}xaxis \\ \Rightarrow x_2=3,y_2=0,z_2=0 \end{gathered}$$

The distance formula is given by $=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}$

$\begin{array}{rcl}& =& \sqrt{{(3-3)}^2+{\left(12-0\right)}^2+{(5-0)}^2}\\ & =& \sqrt{0+144+25}\\ & =& 13\end{array}$

The distance between the two points $(3,12,5)$ and $x$-axis $=13$

Hence, the correct answer is Option (B).