Question: How can I vary the resolution of a simple grid in the x-y plane and obtain the coordinates of the points of intersection?

Good day.

My question involves a set of prescribed points in the Cartesian plane. The x and y ranges are fixed. The points are connected by (imaginary) horizontal and vertical lines to produce a fixed number of blocks / grids.

An example is given in the attached file.  Grid_Example.mw

Now, I wish to reduce the intervals between these points by a scaling factor, n, so as to generate more blocks within the plane that is constrained by the x and y-ranges.

In doing so, I need to find the (x,y)-location of these points in the plane and it would also be great if I could obtain a simple plot.  

As I have several scaling factors to investigate, I was hoping someone may be able to guide me towards a simple routine to help obtain these solutions.

Once again, thanks for taking the time to read this.