1. **State the problem:** We have a rectangle enlarged by a scale factor of $\frac{1}{3}$ with the center of enlargement at the red cross. We need to determine: a) Whether the new rectangle is larger or smaller. b) Which letter marks the vertex on the new rectangle corresponding to vertex $V$. 2. **Understanding scale factor:** A scale factor of $\frac{1}{3}$ means every length from the center of enlargement to a point on the rectangle is multiplied by $\frac{1}{3}$. Since $\frac{1}{3} < 1$, the new rectangle will be smaller than the original. 3. **Finding the corresponding vertex:** The center of enlargement is at the red cross (let's call it $O$). The vertex $V$ is at the bottom-right corner of the rectangle. To find the image of $V$ after enlargement, draw a line from $O$ through $V$ and measure $\frac{1}{3}$ of the distance from $O$ to $V$ along this line. 4. **Using the points on the dotted line:** The points $A, B, C, D, E$ lie on the dotted line through $O$ and $V$ in order from left to right, with $O$ at the bottom-left outside the rectangle. Since $O$ is the center, and $V$ is beyond $E$, the point at $\frac{1}{3}$ distance from $O$ to $V$ will be closer to $O$ than $A$ is. Given the order $A, B, C, D, E, V$, the point corresponding to $V$ after enlargement will be at $C$ because $C$ is approximately one-third along the line from $O$ to $V$. **Final answers:** a) The new rectangle will be smaller than the original. b) The letter $C$ marks the position of the vertex on the new rectangle corresponding to vertex $V$.