Projection of one 2D-rectangle onto another 2D-rectangle I have the following:

http://i.imgur.com/iwOzmxa.png
The center of the blue box is related to the center of the black box. For example, such a relationship could be described such that the black box would be a game's main screen where the red dot is the player, and the blue box would be the map where the red dot is the player on the map. It is just an example.
I'm trying to project any point located within the blue box onto the black box and vice-versa. I basically one to map a coordinate from one of the boxes into the coordinate space of the other.
How can I do this? I wasn't sure what to search online. All the results seem to show how many smaller rectangles fit into a larger one.
I thought about translating the smaller rectangle to the top left corner of the larger one and then somehow stretching the points to match? I'm not sure what I'm thinking or how to start.
Is there any algorithms that can do this or help me?

Assuming that you want the co-ordinates in the blue and black rectangles to be proportionately the same across and down the rectangles, you get $ \frac{X_{blue} - X_S}{X_{S2}-X_S}=\frac{X_{black}-X_L}{X_{L2}-X_L}$ and similarly with $Y$, so
$$X_{blue} = X_S + \left(X_{black}-X_L\right)\frac{X_{S2}-X_S}{X_{L2}-X_L}$$ 
$$Y_{blue} = Y_S + \left(Y_{black}-Y_L\right)\frac{Y_{S2}-Y_S}{Y_{L2}-Y_L}$$ 
$$X_{black} = X_L + \left(X_{blue}-X_L\right)\frac{X_{L2}-X_L}{X_{S2}-X_S}$$ 
$$Y_{black} = Y_L + \left(Y_{blue}-Y_L\right)\frac{Y_{L2}-Y_L}{Y_{S2}-Y_S}$$ 
