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A local park is building a new playground and needs to know how much fencing to buy. The park authority creates a map of the area with the coordinates A(−5,10) , B(1,10) , C(1,−12) , and D(−5,−12) . Each unit on the coordinate plane represents 1 yard. Solve to find out how many yards of fencing is needed (the perimeter).(1 point) Responses 56 yards 56 yards 16 yards 16 yards 12 yards 12 yards 72 yards

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To find the amount of fencing needed for the playground, we can calculate the perimeter of the quadrilateral formed by the points A(−5,10), B(1,10), C(1,−12), and D(−5,−12).

  1. Calculate the lengths of each side:

    • AB: \[ AB = B_x - A_x = 1 - (-5) = 1 + 5 = 6 \text{ yards} \]
    • BC: \[ BC = B_y - C_y = 10 - (-12) = 10 + 12 = 22 \text{ yards} \]
    • CD: \[ CD = C_x - D_x = 1 - (-5) = 1 + 5 = 6 \text{ yards} \]
    • DA: \[ DA = D_y - A_y = -12 - 10 = -12 - 10 = -22 \text{ yards} = 22 \text{ yards (since distance is positive)} \]

  2. Calculate the perimeter: \[ \text{Perimeter} = AB + BC + CD + DA = 6 + 22 + 6 + 22 = 56 \text{ yards} \]

Thus, the total amount of fencing needed is 56 yards.