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)

Question

, 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.

Answer 1

To find the perimeter of the quilt, we need to find the distance between each pair of consecutive points and then add them up.

The distance between points A and B can be found using the distance formula:
AB = √( (1-1)^2 + (-1-4)^2 ) = √(0 + 25) = √25 = 5

The distance between points B and C can be found using the distance formula:
BC = √( (-3-1)^2 + (-1-(-1))^2 ) = √(16 + 0) = √16 = 4

The distance between points C and D can be found using the distance formula:
CD = √( (-1-(-3))^2 + (4-(-1))^2 ) = √(4^2 + 5^2) = √(16 + 25) = √41

The distance between points D and A can be found using the distance formula:
DA = √( (1-(-1))^2 + (4-4)^2 ) = √(2^2 + 0) = √4 = 2

Now, we can add up the distances to find the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 5 + 4 + √41 + 2
Perimeter ≈ 11 + √41 feet

Therefore, the perimeter of the quilt is approximately 11 + √41 feet. William will need this much thread to stitch the quilt to the backing.