To find the perimeter of the polygon formed by the points A, B, C, D, E, and F based on their coordinates, we will first determine the lengths of the sides defined by these points.
The coordinates of the points are:
- A (2, -6)
- B (-5, -6)
- C (-5, 6)
- D (6, 6)
- E (6, 1)
- F (2, 1)
We'll calculate the distances between consecutive points:
-
Distance AB: \[ d_{AB} = \sqrt{(2 - (-5))^2 + (-6 - (-6))^2} = \sqrt{(2 + 5)^2 + (0)^2} = \sqrt{7^2} = 7 \]
-
Distance BC: \[ d_{BC} = \sqrt{(-5 - (-5))^2 + (6 - (-6))^2} = \sqrt{(0)^2 + (6 + 6)^2} = \sqrt{12^2} = 12 \]
-
Distance CD: \[ d_{CD} = \sqrt{(6 - (-5))^2 + (6 - 6)^2} = \sqrt{(6 + 5)^2 + (0)^2} = \sqrt{11^2} = 11 \]
-
Distance DE: \[ d_{DE} = \sqrt{(6 - 6)^2 + (1 - 6)^2} = \sqrt{(0)^2 + (1 - 6)^2} = \sqrt{(-5)^2} = 5 \]
-
Distance EF: \[ d_{EF} = \sqrt{(2 - 6)^2 + (1 - 1)^2} = \sqrt{(-4)^2 + (0)^2} = \sqrt{16} = 4 \]
-
Distance FA: \[ d_{FA} = \sqrt{(2 - 2)^2 + (-6 - 1)^2} = \sqrt{(0)^2 + (-6 - 1)^2} = \sqrt{(-7)^2} = 7 \]
Now, we sum these distances to find the perimeter:
\[ \text{Perimeter} = d_{AB} + d_{BC} + d_{CD} + d_{DE} + d_{EF} + d_{FA} = 7 + 12 + 11 + 5 + 4 + 7 = 46 \]
Thus, the perimeter of the polygon is 46 kilometers.
The correct response is:
46 kilometers.