Find the coordinate of a corner when you know the center, size and rotation

Question

I know the coordinate of the center of an object (box of any size). I also know the rotation of the box and its size.

How could I calculate the position of the top left corner?

I have no math knowledge, and this problem is killing me.

Answer 1

In 2D

The position of $D'$ is

$$\left\{\left(x_1-x_0\right) \cos (\theta )+x_0+\left(y_0-y_1\right) \sin (\theta ),\left(x_1-x_0\right) \sin (\theta )+\left(y_1-y_0\right) \cos (\theta )+y_0\right\}$$