We need to perform a series of transformation on the coordinates of point A.
The original coordinates of this point are:
[tex]A(-3,4)[/tex]The first transformation is a translation 2 units left, and 4 units up. When we translate a coordinate to the left, we need subtract the distance from the x-coordinate, when we translate a coordinate up, we need to add the distance to the y-coordinate, therefore:
[tex]\begin{gathered} A^{\doubleprime}(-3-2,4+4) \\ A^{\doubleprime}(-5,8) \end{gathered}[/tex]Then the figure is dilated by a scale factor of 3, whenever this happens we need to multiply the coordinates of the point by the factor. Therefore we have:
[tex]\begin{gathered} A^{\prime}(-5\cdot3,8\cdot3) \\ A^{\prime}(-15,24) \end{gathered}[/tex]The correct option is the last one.