[tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -2}}\quad ,&{{ 3}})\quad
% (c,d)
&({{ 7}}\quad ,&{{ 9}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[7-(2)]^2+[9-3]^2}\implies d=\sqrt{(7+2)^2+(9-3)^2}
\\\\\\
d=\sqrt{9^2+6^2}\implies d=\sqrt{81+36}\implies d=\sqrt{117}
\\\\\\
\boxed{117=3^2\cdot 13}\qquad \qquad d=\sqrt{3^2\cdot 13}\implies d=3\sqrt{13}[/tex]
