[tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -5}}\quad ,&{{ 6}})\quad
% (c,d)
&({{ 8}}\quad ,&{{ -4}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[8-(-5)]^2+[-4-6]^2}\implies d=\sqrt{(8+5)^2+(-4-6)^2}
\\\\\\
d=\sqrt{13^2+(-10)^2}\implies d=\sqrt{169+100}\implies d=\sqrt{269}[/tex]
