I have a few coordinates that form a triangle. I have a relative point to that triangle. if the coordinates get translated to a new triangle I want to calculate the new relative point. How do I do this generally not only for 2 dimensions but for larger ones too?

```
# triangle translation
(5, 2) -> (2, -3)
(2, -3) -> (-3, 6)
(-3, 6) -> (6, 5)
# relative point
(5, -7) -> (x, y)
```

how do I solve for x, y?

EDIT: as I've done more research into basic geometric transformations I can see that I'm asking for a generalization of all possible transformations of the space. This is not merely a rotation, or a dilation, etc. This particular example rotates the space then stretches it at an increasing rate. So what is the generalized solution for calculating spatial transformations?