Coordinates of a Point in a Shaded Region

As shown, $OM\parallel AB$, and the point $P$ lies in the shaded region bounded by ray $OM$, segment $OB$, and the extension of $AB$ beyond $B$ (boundary excluded). Writing $\overrightarrow{OP}=x\,\overrightarrow{OA}+y\,\overrightarrow{OB}$, determine, with proof, which of the following ordered pairs $(x,y)$ are possible.

1. $\left(\dfrac14,\dfrac34\right)$ 2. $\left(-\dfrac23,\dfrac23\right)$ 3. $\left(-\dfrac14,\dfrac34\right)$ 4. $\left(-\dfrac15,\dfrac75\right)$