Section A.1 Distance Formula
The distance formula is used for finding the distance between two points. In two dimensions it is simply an application of the Pythagorean theorem.
Given two points \((x_1,y_1)\) and \((x_2, y_2)\) the distance between them is:
\begin{equation}
d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\text{.}\label{distance_formula}\tag{A.1.1}
\end{equation}
Extension of the distance formula to three dimensions is straightforward.
\begin{equation}
d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}\label{distance_formula_3d}\tag{A.1.2}
\end{equation}