1. **State the problem:** We have two points on a coordinate plane representing rides in a theme park: the Ferris wheel at $(-5, 4)$ and the roller coaster entrance at $(6, -8)$. We need to find the location of the carousel, which is exactly in the middle, i.e., the midpoint between these two points. 2. **Recall the formula for the midpoint:** The midpoint $M$ between two points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by: $$ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) $$ 3. **Identify the given points:** Ferris wheel: $A(-5, 4)$ Roller coaster entrance: $B(6, -8)$ 4. **Calculate the midpoint coordinates:** Calculate the x-coordinate: $$ \frac{-5 + 6}{2} = \frac{1}{2} = 0.5 $$ Calculate the y-coordinate: $$ \frac{4 + (-8)}{2} = \frac{-4}{2} = -2 $$ 5. **Write the final location of the carousel:** The carousel is located at: $$ \boxed{(0.5, -2)} $$ This means the carousel is slightly to the right of the ticketing office (center) and downwards on the map, consistent with the problem's position hint (bottom-left relative to some reference).