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)

Answer 1

To find the perimeter of the mirror, we need to calculate the distance between each pair of points and then add them up.

1. Distance between points A and B:

Using the distance formula:
AB = sqrt((4-(-3))^2 + (4-4)^2)
= sqrt(7^2 + 0^2)
= sqrt(49)
= 7 feet

2. Distance between points B and C:

Using the distance formula:
BC = sqrt((-3-4)^2 + (4-4)^2)
= sqrt((-7)^2 + 0^2)
= sqrt(49)
= 7 feet

3. Distance between points C and D:

Using the distance formula:
CD = sqrt((-3-(-3))^2 + (4-1)^2)
= sqrt(0^2 + 3^2)
= sqrt(9)
= 3 feet

4. Distance between points D and A:

Using the distance formula:
DA = sqrt((-3-(-3))^2 + (1-4)^2)
= sqrt(0^2 + (-3)^2)
= sqrt(9)
= 3 feet

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

Therefore, Amirah needs to buy a frame for her mirror that is 20 feet long.