To find the perimeter of the backyard, we first need to determine the lengths of the sides formed by the points A, B, C, and D.
The coordinates given are:
- A(-11, 10)
- B(-1, 10)
- C(-1, -10)
- D(-11, -10)
Step 1: Calculate the lengths of each side
-
Length of AB:
- Both points A and B share the same y-coordinate (10), so we can calculate the length using the difference in x-coordinates: \[ AB = |x_B - x_A| = |-1 - (-11)| = |-1 + 11| = |10| = 10 \text{ feet} \]
-
Length of BC:
- Both points B and C share the same x-coordinate (-1), so we can calculate the length using the difference in y-coordinates: \[ BC = |y_C - y_B| = |-10 - 10| = |-20| = 20 \text{ feet} \]
-
Length of CD:
- Both points C and D share the same y-coordinate (-10), so we can calculate the length using the difference in x-coordinates: \[ CD = |x_D - x_C| = |-11 - (-1)| = |-11 + 1| = |-10| = 10 \text{ feet} \]
-
Length of DA:
- Both points D and A share the same x-coordinate (-11), so we can calculate the length using the difference in y-coordinates: \[ DA = |y_A - y_D| = |10 - (-10)| = |10 + 10| = |20| = 20 \text{ feet} \]
Step 2: Calculate the perimeter
Now, we can find the perimeter by adding the lengths of all sides: \[ \text{Perimeter} = AB + BC + CD + DA = 10 + 20 + 10 + 20 = 60 \text{ feet} \]
Final Answer
The perimeter of the backyard is 60 feet.