Question Maya is buying a new desk for her room. She creates a map with the coordinates A(−1,7) , B(1,7) , C(1,−1) , and D(−1,−1) . Each unit on the coordinate plane represents 1 foot. Find the perimeter of her room to help her determine how big of a desk Maya can buy.(1 point)

Answer 1

To find the perimeter of the room represented by the coordinates A(−1, 7), B(1, 7), C(1, −1), and D(−1, −1), we can first identify the shape formed by these points.

1. Identify the distances between the points:

   • The distance between A and B: $$AB=B-A=(1-(-1))=1+1=2\text{ feet (horizontal distance)}$$
   • The distance between B and C: $$BC=C-B=(7-(-1))=7+1=8\text{ feet (vertical distance)}$$
   • The distance between C and D: $$CD=D-C=(1-(-1))=1+1=2\text{ feet (horizontal distance)}$$
   • The distance between D and A: $$DA=A-D=(7-(-1))=7+1=8\text{ feet (vertical distance)}$$

2. Calculate the perimeter: The perimeter $P$ of the room is the sum of the lengths of all sides: $$P=AB+BC+CD+DA=2+8+2+8$$ $$P=20\text{ feet}$$

Thus, the perimeter of Maya's room is 20 feet.