1. The problem involves finding the midpoint and distance between two points on a coordinate plane.
2. The midpoint formula is given by $$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$$ which finds the point exactly halfway between two points $(x_1, y_1)$ and $(x_2, y_2)$.
3. The distance formula is $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ which calculates the straight-line distance between the two points.
4. From the graph, identify the coordinates of the start and finish points. Suppose Start is at $(0,2)$ and Finish is at $(8,8)$.
5. Calculate the midpoint:
$$\left(\frac{0+8}{2}, \frac{2+8}{2}\right) = \left(\frac{8}{2}, \frac{10}{2}\right) = (4, 5)$$
6. Calculate the distance:
$$d = \sqrt{(8-0)^2 + (8-2)^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$$
7. Since each unit on the x-axis corresponds to 0.25 miles, the actual distance is:
$$10 \times 0.25 = 2.5$$ miles.
8. Therefore, the midpoint between Start and Finish is at $(4,5)$ and the distance between them is 2.5 miles.
Midpoint Distance 18D08E
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