I don't think you will find formulas with things like that.

You need define some coordinate system (use the east and north sides as axis) and then find the fence equation.

Then if the fence is dislocated towards SW, this means it is dislocated along a y=x line (considering South and West the positive directions of the axis) and will maintain its slope.

Find the point where that line intersects the fence and calculate the new intersection point in the line after the displacement (point 1 and point 2 should be separated by 10 feet)

After that you get a point and the slope, you can calculate the new equation for the fence and finish it.