Answer:
[tex](35,17)[/tex].
Step-by-step explanation:
The given transformation is
[tex]T_{12,32}[/tex]
Which is a translation [tex](x,y) \implies (x+12,y+32)[/tex]
So, the initial coordinate is (23, -15), with the translation would be
[tex](23, -15) \implies (23+12,-15+32)[/tex]
Therefore, the image of the initial coordinate is [tex](35,17)[/tex].