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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)

1 answer

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.