Since we have no description of the lines AB and CG, all we can do is to generalise.
Two points are always collinear. Therefore AB are collinear. Points C and G can both be collinear, or just one, or neither with respect to AB. If y=ax+b is satisfied by A and B, then C Aand G must also satisfy the same linear equation to be collinear. For lines of finite length it can be argued that points are collinear if they are all on the same line or on that line extended. y=ax+b is a line of infinite length, of which AB is a line segment, then C and G can be regarded as collinear with A and B if they both satisfy y=ax+b.
Three points are always coplanar, so A, B and C or A, B and G are coplanar. The remaining point may not lie in the same plane.
All lines that are not parallel must intersect (if the lines are open ended). Parallel lines (lines with the same slope) don't intersect. Once again if AB and CG are line segments, they may intersect only if they're extended, and that would mean they weren't parallel.