Going from long/lat cords to Geometry or Geography type
Can you cast? No.

geometry and geography are PostGIS types, and your types are likely float, double, or something like that.

Can you create PostGIS types? Yes.

What you want to do is use ST_MakePoint(long,lat).

SELECT *, 
   ST_MakePoint(pickup_longitude, pickup_latitude) as pickup_pt, 
   ST_MakePoint(dropoff_longitude, dropoff_latitude) as dropoff_pt


If you don't have PostGIS.


Get it. Install it. Use it: CREATE EXTENSION postgis;
Or, if you can't get or have a good reason for not wanting it, then and only then should you even consider using the native type, point.

SELECT *, 
   point(pickup_longitude, pickup_latitude) as pickup_pt, 
   point(dropoff_longitude, dropoff_latitude) as dropoff_pt



Geometery vs Geography

Geography to geometry conversions are a function to PostGIS. But you can do it with 

SELECT ST_MakePoint(long,lat)::geography;


Or, you can use another geometery srid with

SELECT ST_SetSRID( ST_MakePoint(long,lat), srid );