So I have two rectangle pictures with known Resolution
On the first image we have a point on $(900, 300)$ $x,y$ pixel coordinate (guessed number, not exactly).
The second picture is rotated by $15^\circ$. Width and Hight of this picture is increased, because its rotated $15^\circ$.
Is there a way to calculate the same point position on the 2nd image with the known information? If yes, how?
Because we are rotating about the center of the image, we will use that as our origin. The relative coordinates of the unrotated point are $(900, 300) - (600, 315) = (300, -15)$. Since we are rotating the point clockwise, we can use the rotation matrix
$$\begin{pmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{pmatrix}$$
as the transformation matrix. Note that $(1, 0)$ gets transformed to $(\cos \theta, -\sin \theta)$ as expected. Here, $\theta = 15^\circ$. So, the image is
$$\begin{pmatrix} \cos (15^\circ) & \sin (15^\circ) \\ -\sin (15^\circ) & \cos (15^\circ) \end{pmatrix} \begin{pmatrix} 300 \\ -15 \end{pmatrix} \approx \begin{pmatrix} 294 \\ -74 \end{pmatrix}$$
when rounded to the nearest integers. Relative to the original origin, the coordinates of the image are about $(600, 315) + (294, -74) = \boxed{(894, 241)}$.
EDIT: Update with new information.
It was given that the coordinates of the (untransformed) center relative to the lower-left of the new image are $(661, 440)$. So, relative to the lower-left of the new image, the point is at $(661, 440) + (294, -74) = \boxed{(955, 366)}$.