Amirah wants to frame her bathroom mirror. She creates a map with the coordinates A(- 3, 4) B(4, 4) C(- 3,4) and D(- 3, 1) Each unit on the coordinate plane represents 1 foot. Find the perimeter of the mirror to determine how big of a frame Amirah needs to buy. (1 point)

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1 answer

The perimeter of the mirror can be calculated by finding the distance between the points A, B, C, and D.

The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we find the distances between the points:
- Distance between points A and B:
d(AB) = √((4 - -3)^2 + (4 - 4)^2) = √(7^2 + 0) = 7 feet

- Distance between points B and C:
d(BC) = √((-3 - 4)^2 + (4 - 4)^2) = √(-7^2 + 0) = 7 feet

- Distance between points C and D:
d(CD) = √((-3 - -3)^2 + (1 - 4)^2) = √(0^2 + (-3)^2) = 3 feet

- Distance between points D and A:
d(DA) = √((-3 - -3)^2 + (1 - 4)^2) = √(0^2 + (-3)^2) = 3 feet

Now, to find the perimeter, we add up all the distances:
Perimeter = AB + BC + CD + DA
Perimeter = 7 + 7 + 3 + 3
Perimeter = 20 feet

Therefore, Amirah needs to buy a frame with a perimeter of 20 feet for her bathroom mirror.