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A high school soccer team is going to Columbus, Ohio to see a professional soccer game. A coordinate grid is superimposed on a highway map of Ohio. The high school is at point (2, 5) and the stadium in Columbus is at point (8, 13). The map shows a highway rest stop halfway between the cities. What is the distance between the high school and the stadium? (One unit = 8.6 miles.)

User Martin Blaustein
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1 Answer

28 votes
28 votes

To find the distance between the high school and the stadium, we need to use the distance formula. The distance formula is given by the following equation:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the coordinates of the starting point, and (x2, y2) is the coordinates of the ending point.

In this case, the starting point is the high school, which is located at the coordinates (2, 5), and the ending point is the stadium in Columbus, which is located at the coordinates (8, 13). Plugging these values into the distance formula, we get:

d = sqrt((8 - 2)^2 + (13 - 5)^2)

d = sqrt(6^2 + 8^2)

d = sqrt(36 + 64)

d = sqrt(100)

d = 10

Therefore, the distance between the high school and the stadium is 10 units. Since 1 unit is equal to 8.6 miles, the distance between the high school and the stadium is 86 miles.

It's worth noting that the rest stop is located halfway between the high school and the stadium. This means that the distance from the high school to the rest stop is 86/2 = 43 miles, and the distance from the rest stop to the stadium is also 43 miles. This can be verified by using the distance formula to find the distance between the rest stop and the high school, and then between the rest stop and the stadium.

User Pete Montgomery
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