[tex]\bf\textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ -2}})\quad
% (c,d)
&({{ 4}}\quad ,&{{ 4}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[4-1]^2+[4-(-2)]^2}\implies d=\sqrt{(4-1)^2+(4+2)^2}
\\\\\\
d=\sqrt{3^2+6^2}\implies d=\sqrt{45}\implies d=\sqrt{3\cdot 3\cdot 5}\implies d=\sqrt{3^2\cdot 5}
\\\\\\
d=3\sqrt{5}[/tex]
