We have to find the slope for the lines AC and DB that are:
[tex]\begin{gathered} ac=\frac{-2-3}{-1-4}=-\frac{5}{3} \\ bd=\frac{3--2}{2--7}=\frac{5}{9} \end{gathered}[/tex]
so we have that the equations are:
[tex]\begin{gathered} 5x+3y=-11 \\ 5x-9y=-17 \end{gathered}[/tex]
having that we get that
[tex]-12y=-6\rightarrow y=0.5\rightarrow5x+1.5=-11\rightarrow x=-\frac{12.5}{5}=-2.5[/tex]
so the answer is (-2.5,0.5)
