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.(1 point)
feet
To find the perimeter of the backyard, we need to calculate the distance between the four coordinates A, B, C, and D and then sum them up.
Distance between A and B:
The x-coordinate of both A and B is -1, so the horizontal distance between them is |-1 - (-11)| = 10 feet.
The y-coordinate of A is 10, and the y-coordinate of B is also 10, so there is no vertical distance between them.
Therefore, the distance between A and B is 10 feet.
Distance between B and C:
The x-coordinate of both B and C is -1, so there is no horizontal distance between them.
The y-coordinate of B is 10, and the y-coordinate of C is -10, so the vertical distance between them is |10 - (-10)| = 20 feet.
Therefore, the distance between B and C is 20 feet.
Distance between C and D:
The x-coordinate of both C and D is -11, so the horizontal distance between them is |-11 - (-1)| = 10 feet.
The y-coordinate of C is -10, and the y-coordinate of D is 10, so the vertical distance between them is |(-10) - 10| = 20 feet.
Therefore, the distance between C and D is 20 feet.
Distance between D and A:
The x-coordinate of D is -11, and the x-coordinate of A is -11, so there is no horizontal distance between them.
The y-coordinate of D is 10, and the y-coordinate of A is 10, so there is no vertical distance between them.
Therefore, the distance between D and A is 0 feet.
Now, we can calculate the perimeter by summing up the distances:
Perimeter = distance between A and B + distance between B and C + distance between C and D + distance between D and A
= 10 + 20 + 20 + 0
= 50 feet
Therefore, the perimeter of the backyard is 50 feet.