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.(1 point)
feet

Answer 1

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.

Answer 2

A contractor is building a new house. She creates a map with the coordinates A(6,12) , B(6,−6) , C(−4,−6) , and D(−4,12) . Each unit on the coordinate plane represents 1 yard. What is the perimeter of the outside of the house?