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)

56 yards

16 yards

72 yards

12 yards

1 answer

To find the perimeter, you need to add up the lengths of all four sides of the playground.

Using the distance formula:
AB = √((1 - (-5))^2 + (10 - 10)^2) = √(36 + 0) = √36 = 6 yards
BC = √((1 - 1)^2 + (-12 - 10)^2) = √(0 + 121) = √121 = 11 yards
CD = √((-5 - 1)^2 + (-12 - (-12))^2) = √(36 + 0) = √36 = 6 yards
AD = √((-5 - (-5))^2 + (10 - (-12))^2) = √(0 + 484) = √484 = 22 yards

Adding up all four sides:
6 + 11 + 6 + 22 = 45 yards

So, the park needs to buy 45 yards of fencing for the new playground.

Therefore, the closest answer choice is 56 yards.