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
To find the perimeter of the mirror, we need to calculate the distance between each pair of points A, B, C, and D.
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
1. Distance between points A and B:
DistanceAB = √((4 - (-3))^2 + (4 - 4)^2)
DistanceAB = √(7^2 + 0^2)
DistanceAB = √49
DistanceAB = 7 feet
2. Distance between points B and C:
DistanceBC = √((4 - (-3))^2 + (4 - 4)^2)
DistanceBC = √(7^2 + 0^2)
DistanceBC = √49
DistanceBC = 7 feet
3. Distance between points C and D:
DistanceCD = √((-3 - (-3))^2 + (1 - 4)^2)
DistanceCD = √(0^2 + (-3)^2)
DistanceCD = √9
DistanceCD = 3 feet
4. Distance between points D and A:
DistanceDA = √((-3 - (-3))^2 + (1 - 4)^2)
DistanceDA = √(0^2 + (-3)^2)
DistanceDA = √9
DistanceDA = 3 feet
Now, we can find the perimeter of the mirror by adding the distances between all pairs of points:
Perimeter = DistanceAB + DistanceBC + DistanceCD + DistanceDA
Perimeter = 7 + 7 + 3 + 3
Perimeter = 20 feet
Therefore, Amirah needs to buy a frame that is at least 20 feet long to frame her bathroom mirror.