A student wants to find the perimeter of their backyard. The student creates a map of their backyard with following coordinates A(−11,10) , B(−1,10) , C(−1,−10) , and D(−11,10) . Each unit on the coordinate plane represents 1 foot. Solve to find the perimeter.
To find the perimeter of the backyard, we need to find the distance between each pair of points A, B, C, and D.
The distance formula to find the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances:
Distance between A and B:
dAB = √((-1 - (-11))^2 + (10 - 10)^2)
dAB = √(10^2 + 0)
dAB = √100
dAB = 10 feet
Distance between B and C:
dBC = √((-1 - (-1))^2 + (10 - (-10))^2)
dBC = √(0^2 + 20^2)
dBC = √400
dBC = 20 feet
Distance between C and D:
dCD = √((-11 - (-1))^2 + (-10 - (-10))^2)
dCD = √((-10)^2 + 0)
dCD = √100
dCD = 10 feet
Distance between D and A:
dDA = √((-11 - (-11))^2 + (10 - (-10))^2)
dDA = √(0^2 + 20^2)
dDA = √400
dDA = 20 feet
Now, we can find the perimeter by adding up the distances:
Perimeter = dAB + dBC + dCD + dDA
Perimeter = 10 + 20 + 10 + 20
Perimeter = 60 feet
Therefore, the perimeter of the student's backyard is 60 feet.