[tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -3}}\quad ,&{{ -6}})\quad
% (c,d)
&({{ 1}}\quad ,&{{ y}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
5=\sqrt{[1-(-3)]^2+[y-(-6)]^2}\implies 5=\sqrt{(1+3)^2+(y+6)^2}
\\\\\\
5=\sqrt{16+y^2+12y+36}\implies 5^2=16+y^2+12y+36
\\\\\\
25=y^2+12y+52\implies 0=y^2+12y+27
\\\\\\
0=(y+9)(y+3)\implies y=
\begin{cases}
-9\\
-3
\end{cases}[/tex]
