Offsetting Rectangle Positions to prevent overlap I have the following cases where rectangles overlap.

I have the coordinates for the intersection rectangle(Blue).
How can i offset the starting coordinates(top-left X-Y) of the 2 rectangles to prevent overlapping,provided that i have the coordinates of the intersection rectangle. 
 A: The answer is that the problems you face depend on which coordinates of the blue intersecting region you have, but no matter what it is in fact impossible without knowing the location of the other rectangles.
If you only have the top left coordinate of the blue region, then the answer is no. Without any other information you are acting within a vacuum. All you know is that the rectangles intersect at some point. You don't know anything other than that. You would have to basically offset them an "infinite" distance apart, because the region of intersection could be anywhere from almost imperceptibly small to any arbitrarily large size.
However, if you have both corners of the blue rectangle you are still screwed. Now by the pictures in your diagram neither rectangle is ever inscribed within the other, and you know that the pink rectangle is to the upper left of the yellow rectangle. In that case if we let $W$ be the width of the blue rectangle and $H$ be the height of the blue rectangle then displacing the yellow rectangle $W + 1$ units right and the $H + 1$ units down will absolutely guarantee that there are no intersections. The "$1$" is a buffer value to prevent the sides from touching. You can optionally drop it if side intersections are allowed.
If the blue rectangle is inscribed, then you are 100% screwed and you would need the coordinates of the pink and yellow rectangles. What it boils down to is the following.
Let us assume such a displacement does in fact exist. Let the width of rectangle yellow be equivalent to one unit on the $x$ axis and let it follow similarly for $y$. This is allowed as we are effectively defining a different coordinate system isometric to the original coordinate system and therefore all abstract (existence of intersections, parallel lines, angles, relative distances, etc.) geometric properties are preserved. We know because the yellow rectangle is inscribed that it has the same coordinates as the blue rectangle. Let us also assume that the yellow rectangle has its top left corner on the origin. Let $U$ and $V$ be the width and height of the pink rectangle. In order to displace the yellow rectangle out of the pink rectangle there must exist a vector $(a,b)$ such that $a \geq U$ and $b \geq V$ and this vector must work for all $(U,V)$ pairs. However, this is equivalent to stating that there exists a real number $a$ such that $a$ is greater than all other real numbers. This is impossible and is a contradiction. Therefore you cannot displace an inscribed rectangle to the outside of another rectangle without knowing the size of the outer rectangle.
For the sake of completeness let us assume you do know the size of the outer rectangle in a situation of full inscription. Then displacing $(U+1,V+1)$ units in the original coordinate system will work to borrow the notation of the proof above.
I'm going to also include that the displacement $(a,b) - (c,d)$ where $(a,b)$ is the bottom right corner of the pink rectangle and $(c,d)$ is the top left corner of the yellow rectangle.
To go any further would require a specific use case of this displacement. Based on that not being included I assume the use case either does not exist or alternatively you only care about displacement in any direction or magnitude so long as intersection ceases. If this is in fact incorrect, then that can be addressed in a future update to this post.
