1. **State the problem:** We have a trapezium with vertex $V$ and a center of enlargement located 2 units below and 1 unit left of $V$. The trapezium is enlarged by a scale factor of 3 from this center. We need to find which letter ($A$, $B$, $C$, or $D$) marks the position of the new vertex corresponding to $V$ after enlargement. 2. **Identify coordinates:** Let the coordinates of $V$ be $(x_V, y_V)$. The center of enlargement $O$ is at $(x_V - 1, y_V - 2)$. 3. **Formula for enlargement:** The coordinates of the image point $V'$ after enlargement with scale factor $k=3$ from center $O$ are given by: $$V' = O + k(V - O)$$ which means $$x_{V'} = x_O + k(x_V - x_O)$$ $$y_{V'} = y_O + k(y_V - y_O)$$ 4. **Calculate $V'$ coordinates:** $$x_{V'} = (x_V - 1) + 3(x_V - (x_V - 1)) = (x_V - 1) + 3(1) = x_V - 1 + 3 = x_V + 2$$ $$y_{V'} = (y_V - 2) + 3(y_V - (y_V - 2)) = (y_V - 2) + 3(2) = y_V - 2 + 6 = y_V + 4$$ 5. **Interpretation:** The new vertex $V'$ is located 2 units to the right and 4 units above the original vertex $V$. 6. **Match with given points:** Among the letters $A$, $B$, $C$, and $D$, the one on the dotted line extending from the center through $V$ and located 2 units right and 4 units up from $V$ is letter $A$. **Final answer:** The vertex of the new trapezium corresponding to $V$ is marked by letter $A$.