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 sum of the lengths of all four sides of the mirror.
Let's calculate the length of each side:
1. Side AB:
Using the distance formula:
AB = √[(4 - (-3))^2 + (4 - 4)^2]
AB = √[7^2 + 0^2]
AB = √(49)
AB = 7 feet
2. Side BC:
Using the distance formula:
BC = √[(4 - 4)^2 + (4 - 1)^2]
BC = √[0^2 + 3^2]
BC = √(9)
BC = 3 feet
3. Side CD:
Using the distance formula:
CD = √[(-3 - (-3))^2 + (1 - 4)^2]
CD = √[0^2 + (-3)^2]
CD = √(9)
CD = 3 feet
4. Side DA:
Using the distance formula:
DA = √[(-3 - 4)^2 + (1 - 4)^2]
DA = √[(-7)^2 + (-3)^2]
DA = √(49 + 9)
DA = √58 feet
Now, let's add up the lengths of all four sides to find the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 7 + 3 + 3 + √58
Perimeter = 13 + √58 feet
Therefore, the perimeter of the mirror is 13 + √58 feet. This is how big of a frame Amirah needs to buy.