\documentclass{standalone}
\usepackage{tikz}


\begin{document}
\begin{tikzpicture}[scale=1.5]
\draw[thin,->] (0,0)--(9.5,0) node[below]{$x'$};
\draw[thin,->] (0,0)--(0,4.2) node[left]{$t'$};

\filldraw[fill=lime] (4.5,3)--(.75,0)--(8.25,0)--(4.5,3);
\fill (4.5,3) circle (.04) node[above] {$(x,t)$};
 
 \node[below] at (.75,0)  {$(x-ct,0)$};
 \node[below] at (8.25,0)  {$(x+ct,0)$};
 
  \node[rotate=38.6598082540901] at (2.1,1.5)  {$x'=x-c(t-t')$};
  \node[rotate=-38.6598082540901] at (7,1.5)  {$x'=x+c(t-t')$};
\node at (4.5,1.5) {$\Delta(x,t)$};

\end{tikzpicture}
\end{document}
