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)
, 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)
feet
To find the perimeter of the quilt, we need to calculate the distance between each pair of coordinates and then add them up.
Let's find the distance between points A and B:
AB = sqrt((1-1)^2 + (4-(-1))^2) = sqrt(0^2 + 5^2) = sqrt(25) = 5 feet
Now, let's find the distance between points B and C:
BC = sqrt((1-(-3))^2 + (-1-(-1))^2) = sqrt(4^2 + 0^2) = sqrt(16) = 4 feet
Next, let's find the distance between points C and D:
CD = sqrt((-3-(-1))^2 + (-1-4)^2) = sqrt((-2)^2 + (-5)^2) = sqrt(4 + 25) = sqrt(29) feet
Finally, let's find the distance between points D and A:
DA = sqrt((-1-1)^2 + (4-4)^2) = sqrt((-2)^2 + 0^2) = sqrt(4) = 2 feet
Now, we can add up all the distances:
Perimeter = AB + BC + CD + DA = 5 + 4 + sqrt(29) + 2 = 11 + sqrt(29) feet
Therefore, the perimeter of the quilt is 11 + sqrt(29) feet.