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
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.