Spinning polygon at plane

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Given a polygon $P$ and some line $l$, Crossing the polygon with some angel $θ$ relative to the $x$ axis, I am Intrested In spinning the polygon, And the line $l$ In such way that the line will be vertical to $x$ axis.

For example, I wish to go from (1) to (2):

Polygon spin

One possible direction I was thinking about Is to add some constans to each of the points of the polygon, But I don't know how to do it correctly.

Any help will be appericiated :)