There is a field on the search screen in Matrix that allows you to search for properties that are new construction (or not).
No means that someone has lived in the house since construction was finished.
Completed means no one has lived in the house since construction was finished.
To Be Built means
Torn Down & Rebuilt means the existing structure was completely torn down and a new one is being built on the existing foundation.
Under Construction means the structure is in the process of being built.