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High school mathematics, plane vector problem, why there is (left plus right MINUS), how to deduce or how to prove it? The vector can be directly in a rectangular coordinate system.
Translation formula

After the point P(x, y) is translated according to the vector (a, b), the corresponding P' coordinate is (x+a, y+b), so there are x = x'-a and y = y'-b.

Substitute x=x'-a and y=y'-b into y=f(x) to get y'-b=f(x'-a).

Because you draw in the xOy coordinate system, the horizontal and vertical variables of the coordinate system are X and Y, so you must write X' as X and Y' as Y, otherwise you can't draw it.

You have y = f (x-a)+b.

So you can see that if a>0 is shifted to the right by one unit, f(x) becomes f(x-a).

If a

So there is left plus right minus.