The transformation that translates the point (4, 5) to the point (12, 13) is:
[tex]T_{(8,8)}[/tex]
Here we will have a translation:
[tex]T_{(a, b)}[/tex]
Such that when applied to a point (x, y) we get:
[tex]T_{(a, b)}(x, y) = (x + a, y + b)[/tex]
Now, let's apply that translation to (4, 5) such that we get (12, 13).
[tex]T_{(a, b)}(4, 5) = (4 + a, 5 + b) = (12, 13)[/tex]
Then we must have:
4 + a = 12
5 + b = 13
Solving for a and b we get:
a = 12 - 4 = 8
b = 13 - 5 = 8
Then the translation is:
[tex]T_{(8,8)}[/tex]
If you want to learn more about translations:
https://brainly.com/question/24850937
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