Subjects algebra

Midpoint Distance 18D08E

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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.