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), 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.
▢ feet
a
To find the perimeter of the quilt, we need to add up the lengths of all the sides.
Using the distance formula, we can find the length of each side:
AB: sqrt[(1-1)^2 + (-1-4)^2] = sqrt(0 + 25) = sqrt(25) = 5 feet
BC: sqrt[(-3-1)^2 + (-1+1)^2] = sqrt((-4)^2 + 0) = sqrt(16) = 4 feet
CD: sqrt[(-1+3)^2 + (4+1)^2] = sqrt(2^2 + 5^2) = sqrt(4 + 25) = sqrt(29) feet
DA: sqrt[(1+1)^2 + (4-4)^2] = sqrt(2^2 + 0) = sqrt(4) = 2 feet
Now we can add up the lengths of all the sides to find the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 5 + 4 + sqrt(29) + 2
Perimeter = 11 + sqrt(29) feet
Therefore, the perimeter of the quilt is approximately 11 + sqrt(29) feet. This is the amount of thread William will need to stitch the quilt to the backing.