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Use the given coordinate to compute the perimeter of the parallelogram.

Coordinates: (-7,5), (6,5), (-9,-2), (4,-2)

A. 40.56 units
B. 29 units
C. 52.3 units
D. 13.3 units

3 answers

To find the perimeter of the parallelogram given the coordinates (-7,5), (6,5), (-9,-2), and (4,-2), we first need to determine the lengths of the sides of the parallelogram.

  1. Identify the vertices:

    • A = (-7, 5)
    • B = (6, 5)
    • C = (4, -2)
    • D = (-9, -2)

  2. Calculate the lengths of the sides:

    • Length AB: Since both points A and B have the same y-coordinate, we can use the formula for the distance between two points: \[ AB = |x_2 - x_1| = |6 - (-7)| = |6 + 7| = 13. \]

    • Length BC: Again, since both points B and C have the same x-coordinate, we can similarly calculate: \[ BC = |y_2 - y_1| = |-2 - 5| = |-7| = 7. \]

  3. Validate side lengths for the parallelogram:

    • Since opposite sides in a parallelogram are equal, we have:
      • Length AD = Length BC = 7
      • Length CD = Length AB = 13

  4. Calculate the perimeter: The perimeter \( P \) of a parallelogram can be calculated using the formula: \[ P = 2(AB + BC) = 2(13 + 7) = 2(20) = 40. \]

Thus, the perimeter of the parallelogram is 40 units.

Therefore, the answer is not among the options given (A. 40.56 units, B. 29 units, C. 52.3 units, D. 13.3 units). Please verify the coordinates if there's an error in the options.

you have to choose one though

I apologize for the oversight in my previous calculation. Based on the calculated perimeter of 40 units, which isn't listed in the choices, we need to assess the closest available option.

Given the choices: A. 40.56 units
B. 29 units
C. 52.3 units
D. 13.3 units

The closest option to 40 units is A. 40.56 units.

Thus, if we must select one from the provided options, the answer is A. 40.56 units.