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 and then add them all up.
Using the distance formula:
Distance between points A and B:
AB = √((4 - (-3))^2 + (4 - 4)^2)
AB = √(7^2 + 0^2)
AB = √49
AB = 7 feet
Distance between points B and D:
BD = √((-3 - 4)^2 + (1 - 4)^2)
BD = √((-7)^2 + (-3)^2)
BD = √(49 + 9)
BD = √58
BD ≈ 7.62 feet
Distance between points D and C:
DC = √((-3 - (-3))^2 + (1 - 4)^2)
DC = √(0^2 + (-3)^2)
DC = √9
DC = 3 feet
Now, we can find the total perimeter by adding up the distances:
Perimeter = AB + BD + DC
Perimeter = 7 + 7.62 + 3
Perimeter ≈ 17.62 feet
Therefore, Amirah needs to buy a frame that is approximately 17.62 feet long to frame her bathroom mirror.