Determining load bearing wall in attached blueprints
The dashed lines that fall along walls and at pillar points in the basement drawing indicate the location of footings (poured structures under the slab). These typically correspond with bearing walls. You'll see some of them labelled "concrete pad". 

I'd expect that the joists running from the wall indicated by the blue arrow to the exterior wall to the right run lengthwise with respect to the home. You can probably verify this a number of ways. If all this is true, you'll need to install a properly-sized beam to carry the floor over that footing. 

The wall indicated by red arrows has a point-load footing under it, as does the more centrally-located wall below it in the drawing. There are probably steel posts and microlam (LVL) beams over the walls there. You'll have to investigate to be sure. The joists in that area probably run crosswise with respect to the home and bear on those beams.