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Understanding rotation of arbitrary points

Problem

The distance between point P and the origin, O, is r units. The line O, P forms an angle of \phi with the x-axis.
Point P, prime is the result of rotating point P, theta degrees counter-clockwise around the origin.
The line A, P, prime forms a right angle with line O, P.
If point P, prime is at left parenthesis, x, prime, comma, y, prime, right parenthesis, y, prime is equal to the length of which line segment?
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