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