Question

Find the distance from $\left(4,-2,6\right)$ to each of the following:

The $x-$axis

Answer 1

To find the distance:

Consider the given point.

$\left(4,-2,6\right)$

The $x-$axis means that the point is $\left(4,0,0\right)$.

Let $\left(x_1,y_1,z_1\right)=\left(4,-2,6\right)$ and $\left(x_2,y_2,z_2\right)=\left(4,0,0\right)$.

Using the distance formula and calculate the distance in below:

$\begin{array}{rcl}\text{d}& =& \sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}\left[\text{Distance formula}\right]\\ & \Rightarrow & \text{d}=\sqrt{{\left(4-4\right)}^2+{\left(0-\left(-2\right)\right)}^2+{\left(0-6\right)}^2}\left[\text{Substitues all values}\right]\\ & \Rightarrow & \text{d}=\sqrt{{\left(0\right)}^2+{\left(2\right)}^2+{\left(-6\right)}^2}\left[\text{Simplifying}\right]\\ & \Rightarrow & \text{d}=\sqrt{0+4+36}\\ & \Rightarrow & \text{d}=\sqrt{40}\\ \therefore \text{d}& =& 2\sqrt{10}\end{array}$

Hence, the distance is $\mathbf{2}\sqrt{\mathbf{10}}$ units.