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.

Answer 1

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.