D

It has the flat 7 note but no 3rd so not the best option for a seventh chord but will be useful from time to time

Based on the D barre chord add the 3 note on the 8th fret and it's a D minor chord

It's in the 4th position becasue that's where your first finger is. Think of it though as based around the 7th fret where the tonic is. A really important chord in the blues.

The barre chord on the 7th fret is a D and can be used for a major or minor because without the 3rd note it is neither.

Another popular voicing because the D is so important in the ksy of G and it's an easy one to grab. It can be played for a major or minor chord because it's neither without the 3.

In the 7th position this shape is a D minor 7th chord, a good one to use whenever you see a minor chord, especially in a blues or jazz tune. Have a listen.

Not a common chord but it sounds good on the 3 string, try using it for a minor chord to jazz up your tunes. A handy moveable shape.

A good seventh chord voicing with the root in the bass and tritone on top. 

This moveable shape is a good option for a 6 chord.

The root in the bass and the third on top, this moveable shape works.