[tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
P&({{ -4}}\quad ,&{{ 3}})\quad
% (c,d)
Q&({{ 6}}\quad ,&{{ 1}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
PQ=\sqrt{[6-(-4)]^2+[1-3]^2}\implies PQ=\sqrt{(6+4)^2+(1-3)^2}
\\\\\\
PQ=\sqrt{10^2+(-2)^2}\implies PQ=\sqrt{100+4}\implies PQ=\sqrt{104}
\\\\\\
PQ=2\sqrt{26}[/tex]
