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 Maya's room, we need to add up the lengths of all four sides.

Using the distance formula, we can find the length of each side:
AB = √((1 - (-1))^2 + (7 - 7)^2) = √(2^2 + 0^2) = √4 = 2 feet
BC = √((1 - 1)^2 + (-1 - 7)^2) = √(0^2 + (-8)^2) = √64 = 8 feet
CD = √((-1 - 1)^2 + (-1 - (-1))^2) = √(-2)^2 + (0)^2) = √4 = 2 feet
DA = √((-1 - (-1))^2 + (-1 - 7)^2) = √(0^2 + (-8)^2) = √64 = 8 feet

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

So, the perimeter of Maya's room is 20 feet. This means she should look for a desk that can fit within these dimensions.