Answer:
The transformation is the function [tex] T : \mathbb{R}^2 \rightarrow \mathbb{R}^2 [/tex] such that [tex] T(x,y)=(x+4,y+3) [/tex], that is, a translation of 4 units right and 3 units up.
Step-by-step explanation:
Notice that if you sum 4 to the first coordinate of the vertices of figure ABC, you will get the first coordinates of figure A'B'C', and if you do the same with second coordinates, but if you sum 3 to them, you will get the second coordinates of figure A'B'C', then, the transformation you are looking for is the one that sums 4 to the first coordinate and 3 to the second coordinate of every point of [tex] \mathbb{R}^2 [/tex].
Then, define a function [tex] T : \mathbb{R}^2 \rightarrow \mathbb{R}^2 [/tex], such that [tex] T(x,y)=(x+4,y+3) [/tex], and that is your translation.
