[tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ 4}})\quad
% (c,d)
&({{ -2}}\quad ,&{{ -1}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{(-2-1)^2+(-1-4)^2}\implies d=\sqrt{(-3)^2+(-5)^2}
\\\\\\
d=\sqrt{9+25}\implies d=\sqrt{34}[/tex]
