I recently subdivided my property into two lots and plan to sell the vacant lot. How do I determine the cost basis for the vacant lot versus the cost basis for my home?

You can use the county appraisal for the percentage allocation but don't use the county's appraisal figures.

Using an example:

You paid $100,000 for the property. In the year your bought it, the tax accessor valued it at $80,000, broken down as $60,000 for the building and $20,000 for the land. So, 25% (20/80 = 25%) of the purchase price was for the land.  0.25 x $100,000 = $25,000.  

1.4acres / 2.2 = 63.6%.  0.636 x $25,00 = $15,909 is your cost basis in the vacant lot sold.  The revised  basis in your home is $100,000 - 15,909 = $84,091.

it depends. where I live appraised values do not represent true FMV. unimproved land gets a high discount while land with a building gets a lower discount. (the discount is not shown just the appraised number).  why not ask a realtor in your area how appraised values are determined.   however, if the appraised value is what you would sell it for, then its likely that is FMV.

Your cost basis has nothing to do with the current value of the land. If you purchased the property, your cost basis is what you paid for it. More recent appraisals and fair market value are not involved in determining your basis. See the example that Hal_Al gave above.