Edit: I'm not sure the original question is clear, so to add some context, this is a computer based puzzle. The user clicks somewhere on the blue area, which produces a pair of x, y coordinates. My goal is to work out which of the numbered tiles was clicked. The coordinate system I want to use has the top left tile as 0, 0, with the first value being the row number and the second being the column number. The rules for the boundaries are not important as long as they are consistent.
I want to map x, y coordinates to grid coordinates (i, j), where the grid is comprised of 50px by 50px, and the origin is at the center. In the image below, that would mean any x, y coords falling between -125 and -75 for x and +50 to +100 for y would map to i=0, j=0 (row 0, column 0).
What is the formula for this mapping please?
Say you have an object that has a local origin $O$ such as the top left point of this tile which would be the point $(-125,50)$ with the top left corner $(0,0)$. Your goal is to describe the position of other objects in the tile relative to that origin.
The second part of the problem is to split the region you're working with up into equally sized rectangles such as the $4$ rows or $5$ columns in your diagram. To do this you need the full size, which is $50$ square pixels. Say you have $I$ rows and $J$ columns. Then you want rectangles of size $50/I$ by $50/J$ pixels. You may have to round these numbers. Lets call $\Delta I = 50/I$ and $\Delta J = 50/J$.
To get the location of each row you'll need to start at the origin, and add some multiple of rows and columns together to get the exact corner. Using your notation this equation would then be of the form $O + (i \Delta I,j \Delta J)$ and there will be one such corner for each of the smaller rectangles in your square tile.