What does distance of a point from line being negative signify? When we take distance from the line, we take
$$ d = \frac{ Ax_o + By_o + C}{ \sqrt{A^2 +B^2}}$$
usually with a modulus on top, now my question is if I evaluate this distance as negative what does it mean? Can I decide on which half-plane a point using this?

The denominator is based on the magnitude of a vector and is always positive, but the numerator is based on the scalar product.  Since the scalar product is based on the cosine ratio, if you find yourself a "negative distance", this just means that the angle between the vector being projected and the normal vector you have decided to use (i.e. $\vec n=(A,B)$ and not $\vec n=(-A, -B)$) is obtuse.
