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
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.