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

16 yards
16 yards

72 yards
72 yards

12 yards
12 yards

56 yards

1 answer

To find the perimeter of the playground, we need to calculate the distance between each pair of adjacent points and then add them up.

The distance between points A and B can be calculated using the distance formula:

dAB = √((x2 - x1)^2 + (y2 - y1)^2)
= √((1 - (-5))^2 + (10 - 10)^2)
= √((6)^2 + (0)^2)
= √(36 + 0)
= √36
= 6 yards

The distance between points B and C can be calculated in the same way:

dBC = √((x2 - x1)^2 + (y2 - y1)^2)
= √((1 - 1)^2 + (-12 - 10)^2)
= √((0)^2 + (-22)^2)
= √(0 + 484)
= √484
= 22 yards

The distance between points C and D can also be calculated in the same way:

dCD = √((x2 - x1)^2 + (y2 - y1)^2)
= √((-5 - 1)^2 + (-12 - (-12))^2)
= √((-6)^2 + (0)^2)
= √(36 + 0)
= √36
= 6 yards

The distance between points D and A can be calculated in the same way:

dDA = √((x2 - x1)^2 + (y2 - y1)^2)
= √((-5 - (-5))^2 + (-12 - 10)^2)
= √((0)^2 + (-22)^2)
= √(0 + 484)
= √484
= 22 yards

Now, we can add up the distances to find the total perimeter:

Perimeter = dAB + dBC + dCD + dDA
= 6 + 22 + 6 + 22
= 56 yards

Therefore, the park will need to buy 56 yards of fencing.