To compute the perimeter of the polygon defined by the given coordinates, we need to find the lengths of each side of the polygon by calculating the distance between each pair of consecutive points. The points in order are:
- Point A: (-2, -4)
- Point B: (-5, 3)
- Point C: (0, 8)
- Point D: (6, 5)
- Point E: (6, -1)
We will also need to include the distance from the last point back to the first to close the polygon.
The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Now we will calculate each side of the polygon:
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Distance AB: \[ d_{AB} = \sqrt{((-5) - (-2))^2 + (3 - (-4))^2} = \sqrt{(-3)^2 + (7)^2} = \sqrt{9 + 49} = \sqrt{58} \approx 7.62 \]
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Distance BC: \[ d_{BC} = \sqrt{(0 - (-5))^2 + (8 - 3)^2} = \sqrt{(5)^2 + (5)^2} = \sqrt{25 + 25} = \sqrt{50} \approx 7.07 \]
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Distance CD: \[ d_{CD} = \sqrt{(6 - 0)^2 + (5 - 8)^2} = \sqrt{(6)^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45} \approx 6.71 \]
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Distance DE: \[ d_{DE} = \sqrt{(6 - 6)^2 + (-1 - 5)^2} = \sqrt{(0)^2 + (-6)^2} = \sqrt{0 + 36} = \sqrt{36} = 6.0 \]
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Distance EA: \[ d_{EA} = \sqrt{((-2) - 6)^2 + (-4 - (-1))^2} = \sqrt{(-8)^2 + (-3)^2} = \sqrt{64 + 9} = \sqrt{73} \approx 8.54 \]
Now we sum all these distances to find the perimeter:
\[ \text{Perimeter} = d_{AB} + d_{BC} + d_{CD} + d_{DE} + d_{EA} \] \[ \text{Perimeter} \approx 7.62 + 7.07 + 6.71 + 6.0 + 8.54 \approx 35.94 \]
Rounding to the nearest whole number gives approximately \( 36 \) units.
Thus, the answer is: B. 36 units.
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