William is getting ready to enter his quilt into a competition at the state fair before he enters a quilt he needs to stitch the top of the quilt into 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

Answer 1

To find the perimeter of the quilt, we need to calculate the distance between each pair of adjacent points and sum them up.

The distance formula between two points (x1, y1) and (x2, y2) is:
√((x2-x1)^2 + (y2-y1)^2)

So, let's calculate the distance between the points:
AB = √((1-1)^2 + (-1-4)^2)
AB = √(0^2 + (-5)^2)
AB = √25
AB = 5 feet

BC = √((-3-1)^2 + (-1-(-1))^2)
BC = √((-4)^2 + 0^2)
BC = √16
BC = 4 feet

CD = √((-1-(-3)^2 + (4-(-1))^2)
CD = √((-4)^2 + 5^2)
CD = √16 + 25
CD = √41
CD ≈ 6.4 feet

DA = √((1-(-1))^2 + (4-4)^2)
DA = √(2^2 + 0^2)
DA = √4
DA = 2 feet

Now, sum up the distances to find the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 5 + 4 + 6.4 + 2
Perimeter = 17.4 feet

So, the perimeter of William's quilt is 17.4 feet. This is the amount of thread he will need to stitch the quilt to the backing.