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.

Answer 1

To find the perimeter of the room, we need to calculate the sum of the lengths of all four sides.

Using the distance formula, the distance between points A and B is given by:
AB = √[(1 - (-1))^2 + (7 - 7)^2]
AB = √[2^2 + 0^2]
AB = √(4)
AB = 2

Similarly, the distance between points B and C is given by:
BC = √[(1 - 1)^2 + (-1 - 7)^2]
BC = √[0^2 + (-8)^2]
BC = √64
BC = 8

The distance between points C and D is given by:
CD = √[(-1 - 1)^2 + (-1 - (-1))^2]
CD = √[(-2)^2 + 0^2]
CD = √(4)
CD = 2

Finally, the distance between points D and A is given by:
DA = √[(-1 -(-1))^2 + (-1 - 7)^2]
DA = √[0^2 + (-8)^2]
DA = √64
DA = 8

Now, we sum up the lengths of all sides to find the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 2 + 8 + 2 + 8
Perimeter = 20 feet

Therefore, the perimeter of Maya's room is 20 feet. She can use this information to determine the maximum size of desk she can buy to fit in her room.