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 consecutive points A, B, C, D and add them up.
Using the distance formula d = √((x2-x1)^2 + (y2-y1)^2):
1. Distance between points A and B:
d1 = √((-1 - (-11))^2 + (10 - 10)^2)
= √(10^2 + 0)
= √100
= 10 feet
2. Distance between points B and C:
d2 = √((-1 - (-1))^2 + (-10 - 10)^2)
= √(0 + (-20)^2)
= √400
= 20 feet
3. Distance between points C and D:
d3 = √((-11 - (-1))^2 + (-10 - 10)^2)
= √((-10)^2 + (-20)^2)
= √(100 + 400)
= √500
= 10√5 feet
4. Distance between points D and A:
d4 = √((-11 - (-11))^2 + (10 - (-10))^2)
= √(0 + 20^2)
= √400
= 20 feet
Now, add the distances together to find the perimeter:
Perimeter = d1 + d2 + d3 + d4
Perimeter = 10 + 20 + 10√5 + 20
Perimeter = 30 + 20√5
Therefore, the perimeter of the backyard is 30 + 20√5 feet.
wrong
Let's correct the calculation:
1. Distance between points A and B:
d1 = √((-1 - (-11))^2 + (10 - 10)^2)
= √(10^2 + 0)
= √100
= 10 feet
2. Distance between points B and C:
d2 = √((-1 - (-1))^2 + (-10 - 10)^2)
= √(0 + (-20)^2)
= √400
= 20 feet
3. Distance between points C and D:
d3 = √((-11 - (-1))^2 + (-10 - 10)^2)
= √((-10)^2 + (-20)^2)
= √(100 + 400)
= √500
= 10√5 feet
4. Distance between points D and A:
d4 = √((-11 - (-1))^2 + (10 - (-10))^2)
= √((-10)^2 + 20^2)
= √(100 + 400)
= √500
= 10√5 feet
Now, add the distances together to find the perimeter:
Perimeter = d1 + d2 + d3 + d4
Perimeter = 10 + 20 + 10√5 + 10√5
Perimeter = 30 + 20√5
Therefore, the correct perimeter of the backyard is 30 + 20√5 feet.