Question: Can someone provide an explanation for why translation is not a linear transform?

PandaX

Suppose we want to translate point x by vector t.
f(x+y) = (x+y) + t
f(x) + f(y) = (x+t)+(y+t) = (x+y) + 2t
so it does not correspond to the definition of linear transform.

Question:Can someone provide an explanation for why translation is not a linear transform?Suppose we want to translate point x by vector t. f(x+y) = (x+y) + t f(x) + f(y) = (x+t)+(y+t) = (x+y) + 2t so it does not correspond to the definition of linear transform.