A contractor is building a new house. She creates a map with the coordinates A(6,12)

Question

, B(6,−6)
, C(−4,−6)
, and D(−4,12)
. Each unit on the coordinate plane represents 1 yard. What is the perimeter of the outside of the house?(1 point)
yards

Answer 1

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

Using the distance formula:

AB = √((6-6)^2 + (-6-12)^2) = √(0^2 + (-18)^2) = √(0 + 324) = √324 = 18 yards
BC = √((6+4)^2 + (-6+6)^2) = √(10^2 + 0^2) = √(100 + 0) = √100 = 10 yards
CD = √((-4+4)^2 + (12+6)^2) = √(0^2 + 18^2) = √(0 + 324) = √324 = 18 yards
DA = √((-4-6)^2 + (12-12)^2) = √((-10)^2 + 0^2) = √(100 + 0) = √100 = 10 yards

Adding these up:
18 + 10 + 18 + 10 = 56

Therefore, the perimeter of the outside of the house is 56 yards.

Answer 2

A student wants to find the perimeter of their backyard. The student creates a map of their backyard with following coordinates A(−11,10)
, B(−1,10)
, C(−1,−10)
, and D(−11,10)
. Each unit on the coordinate plane represents 1 foot. Solve to find the perimeter.(1 point)
feet

Answer 3

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

Using the distance formula:

AB = √((-1 + 11)^2 + (10 - 10)^2) = √(10^2 + 0^2) = √(100) = 10 feet
BC = √((-1 + 1)^2 + (-10 - 10)^2) = √(0^2 + (-20)^2) = √(0 + 400) = √400 = 20 feet
CD = √((-11 + 1)^2 + (-10 + 10)^2) = √(-10^2 + 0^2) = √(100 + 0) = √100 = 10 feet
DA = √((-11 + 11)^2 + (10 - (-10))^2) = √(0^2 + 20^2) = √(0 + 400) = √400 = 20 feet

Adding these up:
10 + 20 + 10 + 20 = 60

Therefore, the perimeter of the backyard is 60 feet.