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
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.