Draw a triangle that encloses points

Question

Consider the following TikZ code.

\begin{tikzpicture}
    \node[circle,fill=red] (1) at (4,7.5)  {};
    \node[circle,fill=green ] (2) at (8,8)  {};
    \node[circle,fill=blue] (4) at (5,7)  {};
    \node[circle,fill=violet] (3) at (8,5)  {};
    \node[circle,fill=orange] (5) at (9,4.5)  {};
    
    \node[circle,fill=red] (11) at (2,4)  {};
    \node[circle,fill=green ] (22) at (4,5)  {};
    \node[circle,fill=blue] (44) at (5,4)  {};
    \node[circle,fill=violet] (33) at (1,8)  {};
    \node[circle,fill=orange] (55) at (3,6.5)  {};
\end{tikzpicture}

That produce the following

I want to draw two triangles as follows

How we can draw those?

Answer 1

If I compile this:

\documentclass[12pt]{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
    \node[circle,fill=red] (1) at (4,7.5)  {};
    \node[circle,fill=green ] (2) at (8,8)  {};
    \node[circle,fill=blue] (4) at (5,7)  {};
    \node[circle,fill=violet] (3) at (8,5)  {};
    \node[circle,fill=orange] (5) at (9,4.5)  {};
    \draw[thick,color=red] (10,3)--(8,9)--(2.5,8)--(10,3);
    
    \node[circle,fill=red] (11) at (2,4)  {};
    \node[circle,fill=green ] (22) at (4,5)  {};
    \node[circle,fill=blue] (44) at (5,4)  {};
    \node[circle,fill=violet] (33) at (1,8)  {};
    \node[circle,fill=orange] (55) at (3,6.5)  {};
    \draw[thick,color=red] (-1,10)--(9.5,3)--(2,3)--(-1,10);
  \end{tikzpicture}
\end{document}

what I get is this: