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Method B1

Here we shift the invariant line 1 unit up, so A and B have coordinates (0, 8) and (1, 8).

You might be surprised by the resulting position of the green image:
why is it just 1 unit lower, rather than 2 ?

What happens to the area of the image? That's not a surprise ...

Next we lower A so that the invariant like has a gradient of 1 (ie is at an angle of 45˚).