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
To find the perimeter of the quilt, we need to add up the lengths of all the sides.
Side AB:
√((1-1)^2 + (4-(-1))^2) = √(0^2 + 5^2) = √25 = 5 feet
Side BC:
√((-3-1)^2 + (-1-(-1))^2) = √((-4)^2 + 0^2) = √16 = 4 feet
Side CD:
√((-1-(-3))^2 + (4-(-1))^2) = √(2^2 + 5^2) = √29 = approximately 5.39 feet
Side DA:
√((1-(-1))^2 + (4-4)^2) = √(2^2 + 0^2) = √4 = 2 feet
Now, add up the lengths of all the sides to find the perimeter:
5 feet + 4 feet + 5.39 feet + 2 feet = 16.39 feet
Therefore, the perimeter of the quilt is approximately 16.39 feet. This is how much thread William will need to stitch the quilt to the backing.
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
To find the perimeter of the quilt, we need to calculate the distance between each pair of consecutive points and then add up those distances.
Distance between points A and B:
√((1-1)^2 + (4-(-1))^2) = √(0^2 + 5^2) = √25 = 5 feet
Distance between points B and C:
√((1-(-3))^2 + (-1-(-1))^2) = √(4^2 + 0^2) = √16 = 4 feet
Distance between points C and D:
√((-3-(-1))^2 + (-1-4)^2) = √((-2)^2 + (-5)^2) = √(4 + 25) = √29 = approximately 5.39 feet
Distance between points D and A:
√((-1-1)^2 + (4-4)^2) = √(0^2 + 0^2) = √0 = 0 feet
Now, we add up all these distances:
5 feet + 4 feet + 5.39 feet + 0 feet = 14.39 feet
Therefore, the perimeter of the quilt is approximately 14.39 feet. This is how much thread William will need to stitch the quilt to the backing.