Given:
point P(2,3)
point P'(5,- 4)
So, the translation is:
[tex]\begin{gathered} (x,y)\Rightarrow(x+3,y-7) \\ \text{for P} \\ (2+3,3-7)=(5,-4)\text{ point given} \end{gathered}[/tex]Therefore the image of (6, -2) is:
[tex](6+3,-2-7)=(9,-9)[/tex]Answer: (9,-9)