William is getting ready to enter his quilt into a competition at the state fair. Before he enters the quilt, he needs to stitch the top of the quilt to the backing. He created a map of the quilt with the coordinates A(1,4)

, B(1,−1)
, C(−3,−1)
, and D(−1,4)
. Each unit on the coordinate plane represents 1 foot. Find the perimeter of the quilt in order to determine how much thread William will need to stitch the quilt to the backing.(1 point)
feet

5 answers

To find the perimeter of the quilt, we need to calculate the sum of the lengths of all four sides.

AB = √((1-1)^2 + (-1-4)^2) = √(0 + 25) = 5 feet

BC = √((-3-1)^2 + (-1-(-1))^2) = √(16 + 0) = 4 feet

CD = √((-1+3)^2 + (4+1)^2) = √(4 + 9) = √13 feet

DA = √((1+1)^2 + (4-4)^2) = √(4 + 0) = 2 feet

Therefore, the perimeter of the quilt is:

AB + BC + CD + DA = 5 + 4 + √13 + 2 = 11 + √13 feet

So, William will need 11 + √13 feet of thread to stitch the quilt to the backing.
wrong
I apologize for the error. Let's recalculate the perimeter of the quilt:

To find the perimeter, we need to add the lengths of all four sides:

AB = √((1-1)^2 + (-1-4)^2) = √(0 + 25) = √25 = 5 feet

BC = √((-3-1)^2 + (-1-(-1))^2) = √((-4)^2 + 0) = √16 = 4 feet

CD = √((-1-(-3))^2 + (4-(-1))^2) = √(2^2 + 5^2) = √(4 + 25) = √29 feet

DA = √((1-(-1))^2 + (4-4)^2) = √(2^2 + 0) = √4 = 2 feet

Now, we add up all four sides to find the perimeter:

Perimeter = AB + BC + CD + DA
Perimeter = 5 + 4 + √29 + 2
Perimeter = 11 + √29 feet

Therefore, the correct perimeter of the quilt is 11 + √29 feet. This is the distance that William needs to stitch, and the amount of thread he will need for the job.
wrong
I apologize for the mistake. Let's recalculate the perimeter of the quilt with the given coordinates:

To find the perimeter, we need to add the lengths of all four sides:

AB = √((1-1)^2 + (-1-4)^2) = √(0 + 25) = √25 = 5 feet

BC = √((-3-1)^2 + (-1-(-1))^2) = √((-4)^2 + 0) = √16 = 4 feet

CD = √((-1-(-3))^2 + (4-(-1))^2) = √(2^2 + 5^2) = √(4 + 25) = √29 feet

DA = √((1-(-1))^2 + (4-4)^2) = √(2^2 + 0) = √4 = 2 feet

Now, we add up all four sides to find the correct perimeter:

Perimeter = AB + BC + CD + DA
Perimeter = 5 + 4 + √29 + 2
Perimeter = 11 + √29 feet

Therefore, the correct perimeter of the quilt is 11 + √29 feet. This is the distance that William needs to stitch and the amount of thread he will need for the job.