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The middle school is located at (0, 0) on a coordinate plane. Town Hall is located 4 miles directly east of the middle school. The fire station is located 2 miles directly north of Town Hall.
How many miles long is a straight line between the school and the fire station? Round to the nearest tenth.
miles
To find the distance between the middle school and the fire station, we first need to determine their coordinates based on the problem description.
1. The middle school is at (0, 0).
2. Town Hall is located 4 miles directly east of the middle school. Therefore, its coordinates are (4, 0).
3. The fire station is located 2 miles directly north of Town Hall. This means we add 2 miles to the y-coordinate of Town Hall: (4, 2).
Now we have the coordinates:
– Middle School: (0, 0)
– Fire Station: (4, 2)
To find the straight-line distance between these two points, we can use the distance formula:
[
d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
]
where ((x_1, y_1)) = (0, 0) and ((x_2, y_2)) = (4, 2).
Let’s plug in the values:
[
d = sqrt{(4 – 0)^2 + (2 – 0)^2}
]
[
d = sqrt{4^2 + 2^2} = sqrt{16 + 4} = sqrt{20}
]
Calculating (sqrt{20}):
[
sqrt{20} approx 4