To find the perimeter of the polygon formed by the points A, B, C, D, E, and F on the coordinate plane, we first need to determine the distances between each pair of consecutive points. We will then add these distances to get the total perimeter.
The coordinates of the points are:
- A (2, -6)
- B (-5, -6)
- C (-5, 6)
- D (6, 6)
- E (6, 1)
- F (2, 1)
Now let's calculate the distances between consecutive points.
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Distance AB: \[ \sqrt{((-5 - 2)^2 + (-6 - (-6))^2)} = \sqrt{(-7)^2 + 0^2} = \sqrt{49} = 7 \]
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Distance BC: \[ \sqrt{((-5 - (-5))^2 + (6 - (-6))^2)} = \sqrt{0^2 + (12)^2} = \sqrt{144} = 12 \]
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Distance CD: \[ \sqrt{((6 - (-5))^2 + (6 - 6)^2)} = \sqrt{(11)^2 + 0^2} = \sqrt{121} = 11 \]
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Distance DE: \[ \sqrt{((6 - 6)^2 + (1 - 6)^2)} = \sqrt{0^2 + (-5)^2} = \sqrt{25} = 5 \]
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Distance EF: \[ \sqrt{((2 - 6)^2 + (1 - 1)^2)} = \sqrt{(-4)^2 + 0^2} = \sqrt{16} = 4 \]
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Distance FA: \[ \sqrt{((2 - 2)^2 + (-6 - 1)^2)} = \sqrt{0^2 + (-7)^2} = \sqrt{49} = 7 \]
Now we can find the total perimeter (P) by adding all the distances: \[ P = AB + BC + CD + DE + EF + FA = 7 + 12 + 11 + 5 + 4 + 7 = 46 \]
Therefore, the perimeter of the polygon is 46 kilometers.
The correct response is: 46 kilometers.