Answer: 0
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Explanation:
The term "variant" means "it changes" or "it moves location".
So "invariant" means it stays fixed in place.
The translation vector [tex]\binom{1}{3}[/tex] is the same as writing the rule [tex](x,y) \to (x+1,y+3)[/tex]. It says to shift every (x,y) point 1 unit to the right and 3 units up. The key to this is the "every". There isn't a point left out that the translation doesn't touch. No points stay fixed in place. There are no invariant points.
In contrast, if we were to do a dilation, then the invariant point is the center of the dilation. Everything either shrinks or enlarges with respect to this fixed center point. Another example would be a rotation where the center of rotation stays fixed. Unfortunately, translations do not have this property of having an invariant fixed point.
