On $\triangle ABC$, point $A$ is located at $(3, 5)$ and point $B$ is located at $(-1, 2)$. Point $C$ is located a distance of $3$ from the origin. Given that the area of $\triangle ABC$ is $4$, the coordinates of point $C$ can be expressed in the form of $(a, b)$, where $a$ and $b$ are real numbers. Find $|1200a – 1600b|$.
You may use a five-function calculator ($+, -, \times, \div, \sqrt{\;}$), but one is not required.