Question

Please help I'm kinda confused-​

Answer 1

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 $\binom{1}{3}$ is the same as writing the rule $(x,y) \to (x+1,y+3)$. 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.