To create a graph of the triangle formed by the points \((1, -1)\), \((-0.5, 0.5)\), and \((1, 2)\) and to prove that it is isosceles, you can use the following LaTeX code with the `tikz` package for the graph and some mathematical reasoning for the proof.
```latex
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{center}
% Drawing the graph
\begin{tikzpicture}[scale=1.5]
% Draw axes
\draw[->]