Translate point after rotation relative to different origin

Question

I have 200x380 input image and coordinates (63,146) where (0,0) is top-left:

I rotate about the centre some amount of degrees and expand the "canvas" to avoid cropping resulting in larger output image:

How do I calculate the relative position of point after rotation, with respect to the new larger image?

I'm roughly familiar with how to get the point with respect to the original size but I'm not sure how to transform the calculated new point to fit it in the new image. Red dot is failed attempt of implementing solution transforming the images centre to the 0,0 used in the rotation transform:

My math literacy is not fantastic and I apologise for misusing any terms.

Answer 1

Turns out the solution lies in knowing the correct terms to google for.

Put exact implementation here into a function for individual points, using same rotation matrix returned by the image rotate function solved the problem:

def rotate_single_point(point_tuple, rotation_matrix):
    # https://stackoverflow.com/a/38794480/2244284
    # points
    points = np.array([[point_tuple[0],  point_tuple[1]]])
    # add ones
    ones = np.ones(shape=(len(points), 1))
    points_ones = np.hstack([points, ones])
    # transform points
    transformed_points = rotation_matrix.dot(points_ones.T).T
    return transformed_points