Step-by-Step Solution
Key Concept: For any triangle, the orthocentre, centroid, and circumcentre are collinear (Euler line) with $H = 3G - 2O$.
With circumcentre $O$ at $(4, 3)$ and centroid $G = (\frac{17}{3}, \frac{1}{3})$, the orthocentre is found using Euler's line relation: $H = 3G - 2O$. Substituting: $H = 3(\frac{17}{3}, \frac{1}{3}) - 2(4, 3) = (17, 1) - (8, 6) = (9, -5)$.
Correct Answer: 3