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 56 yards 56 yards 12 yards 12 yards 72 yards
To find the perimeter of the shape formed by the coordinates A, B, C, and D, we need to add up the lengths of all four sides.
Side AB:
Length = sqrt((1-(-5))^2 + (10-10)^2) = sqrt(6^2) = 6 yards
Side BC:
Length = sqrt((1-1)^2 + (-12-10)^2) = sqrt((-22)^2) = 22 yards
Side CD:
Length = sqrt((-5-1)^2 + (-12-(-12))^2) = sqrt((-6)^2) = 6 yards
Side DA:
Length = sqrt((-5-(-5))^2 + (-12-10)^2) = sqrt(6^2) = 6 yards
Now, add up all the sides:
Perimeter = 6 + 22 + 6 + 6 = 40 yards
Therefore, 40 yards of fencing is needed for the playground.