[tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ 1}}\quad ,&{{ 5}})\quad
% (c,d)
B&({{ 4}}\quad ,&{{ 1}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
AB=\sqrt{(4-1)^2+(1-5)^2}\implies AB=\sqrt{3^2+(-4)^2}
\\\\\\
AB=\sqrt{9+16}\implies AB=\sqrt{25}\implies AB=5[/tex]
