[tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
M&({{ 0}}\quad ,&{{ 6}})\quad
% (c,d)
N&({{ 5}}\quad ,&{{ 3}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
MN=\sqrt{(5-0)^2+(3-6)^2}\implies MN=\sqrt{5^2+(-3)^2}
\\\\\\
MN=\sqrt{25+9}\implies \boxed{MN=\sqrt{34}}\\\\ [/tex]
[tex]\bf -------------------------------\\\\
\textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
R&({{-7}}\quad ,&{{ -5}})\quad
% (c,d)
S&({{ -2}}\quad ,&{{ -2}})
\end{array}\quad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
RS=\sqrt{[-2-(-7)]^2+[-2-(-5)]^2}
\\\\\\
RS=\sqrt{(-2+7)^2+(-2+5)^2}\implies RS=\sqrt{5^2+3^2}
\\\\\\
RS=\sqrt{25+9}\implies \boxed{RS=\sqrt{34}}[/tex]
well, are they?
