I have my Group Theory exam in less than a month and I can't get to grips with orbits and stabilizers. Please could someone talk me through the solution to this question?

Let G=GL(2,\mathbb R) and X=\mathbb R^{2}.

Let G\times X\rightarrow X, <br />
\left(\begin{array}{ccc}<br />
 \left(\begin{array}{cc}<br />
 a & b\\<br />
 c & d\end{array}\right) & , & \left(\begin{array}{c}<br />
 x\\<br />
 y\end{array}\right)\end{array}\right)\mapsto\left(  \begin{array}{ccc}<br />
 ax & + & by\\<br />
 cx & + & dy\end{array}\right),<br />
define a G action.

What are the orbits and fixed point sets of this G action?