In order to translate 5 units to the left and 3 units up, we need to decrease 5 units of the x-coordinate and increase 3 units of the y-coordinate.
Looking at the graph, the coordinates of point P are (3, -4).
So, subtracting 5 units from the x-coordinate and adding 3 units to the y-coordinate, we have:
[tex]\begin{gathered} P(3,-4)\\ \\ P^{\prime}(3-5,-4+3)=P^{\prime}(-2,-1) \end{gathered}[/tex]
Therefore the image of point P after the translation is located at (-2, -1).
