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
12 yards
12 yards
72 yards
72 yards
56 yards
56 yards
16 yards
Response: 16 yards
To find the perimeter of the playground, we need to add up the lengths of all four sides.
Side AB = sqrt((1 - (-5))^2 + (10 - 10)^2) = 6 yards
Side BC = sqrt((1 - 1)^2 + (-12 - 10)^2) = 22 yards
Side CD = sqrt((-5 - 1)^2 + (-12 - (-12))^2) = 6 yards
Side DA = sqrt((-5 - (-5))^2 + (-12 - 10)^2) = 22 yards
Adding up all four sides, we get: 6 + 22 + 6 + 22 = 56 yards.
Therefore, 56 yards of fencing is needed.