To find the perimeter of the quilt, we need to calculate the distance between each pair of consecutive points and then add them up.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances between the points:
AB: dAB = sqrt((1 - 1)^2 + (-1 - 4)^2) = sqrt(0 + 25) = 5 feet
BC: dBC = sqrt((-3 - 1)^2 + (-1 - (-1))^2) = sqrt(16 + 0) = 4 feet
CD: dCD = sqrt((-1 - (-3))^2 + (4 - (-1))^2) = sqrt(4 + 25) = 5 feet
DA: dDA = sqrt((1 - (-1))^2 + (4 - 4)^2) = sqrt(4 + 0) = 2 feet
Now, we add up the distances to get the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 5 + 4 + 5 + 2
Perimeter = 16 feet
Therefore, William will need 16 feet of thread to stitch the quilt to the backing.
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)
1 answer