To calculate the perimeter of the parallelogram defined by the given coordinates, we first need to find the lengths of the sides.
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Calculate the length of side AB:
- A = (-5, -4)
- B = (2, -4)
- The length is calculated using the distance formula: \[ \text{Length of AB} = |x_2 - x_1| = |2 - (-5)| = |2 + 5| = 7 \text{ units} \]
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Calculate the length of side AD:
- A = (-5, -4)
- D = (4, 2)
- The length is calculated using the distance formula: \[ \text{Length of AD} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(4 - (-5))^2 + (2 - (-4))^2} \] \[ = \sqrt{(4 + 5)^2 + (2 + 4)^2} = \sqrt{9^2 + 6^2} = \sqrt{81 + 36} = \sqrt{117} \approx 10.82 \text{ units} \]
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Now calculate the perimeter of the parallelogram:
- The perimeter \( P \) of a parallelogram is given by: \[ P = 2(\text{length of AB} + \text{length of AD}) = 2(7 + 10.82) = 2(17.82) \approx 35.64 \text{ units} \]
Since we are looking for specific values in the response options and while I have calculated the perimeter to be approximately 35.64 units, the closest value among the options given is not found here.
This suggests an error in either calculation or interpretation of the coordinates to represent a parallelogram, or possibly that the expected answers do not align with our calculations.
Final answer: None of the provided options are correct based on the length calculations.
1 answer