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 calculate the distance between each pair of coordinates and then sum them up.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)² + (y2 - y1)²)
Let's calculate the distances for the given coordinates:
1. Distance between A(-11, 10) and B(-1, 10):
Distance AB = √((-1 - (-11))² + (10 - 10)²)
= √(10² + 0)
= √100
= 10 ft
2. Distance between B(-1, 10) and C(-1, -10):
Distance BC = √((-1 - (-1))² + (-10 - 10)²)
= √(0² + (-20)²)
= √400
= 20 ft
3. Distance between C(-1, -10) and D(-11, -10):
Distance CD = √((-11 - (-1))² + (-10 - (-10))²)
= √((-10)² + 0)
= √100
= 10 ft
4. Distance between D(-11, -10) and A(-11, 10):
Distance DA = √((-11 + 11)² + (10 - (-10))²)
= √(0² + 20²)
= √400
= 20 ft
Now, we can find the perimeter by summing up the distances: Perimeter = AB + BC + CD + DA = 10 ft + 20 ft + 10 ft + 20 ft = 60 ft
Therefore, the perimeter of the backyard is 60 feet.