Question
Question 2: Use the coordinate plane below to solve the problem . Also use page 8 of 13 for help.
A room is mapped with coordinates:
A (5,–2), B (–5,–2), C (–5,7), and D (5,7).
Each unit of the coordinate plane represents a meter. Find the number of meters of crown molding needed to place around the room (perimeter).
Answers
GPT 3.5
To find the perimeter of the room, we need to add up the lengths of all four sides.
Side AB:
Using the distance formula:
AB = √[(-5 - 5)^2 + (-2 - (-2))^2]
AB = √[(-10)^2 + (0)^2]
AB = √[100 + 0]
AB = √100
AB = 10 meters
Side BC:
Using the distance formula:
BC = √[(-5 - (-5))^2 + (7 - (-2))^2]
BC = √[0^2 + 9^2]
BC = √0 + 81
BC = √81
BC = 9 meters
Side CD:
Using the distance formula:
CD = √[(5 - (-5))^2 + (7 - 7)^2]
CD = √[(10)^2 + 0^2]
CD = √100 + 0
CD = √100
CD = 10 meters
Side DA:
Using the distance formula:
DA = √[(5 - 5)^2 + (7 - (-2))^2]
DA = √[0^2 + 9^2]
DA = √0 + 81
DA = √81
DA = 9 meters
Now, to find the perimeter of the room:
Perimeter = AB + BC + CD + DA
Perimeter = 10 + 9 + 10 + 9
Perimeter = 38 meters
Therefore, 38 meters of crown molding is needed to place around the room.
Side AB:
Using the distance formula:
AB = √[(-5 - 5)^2 + (-2 - (-2))^2]
AB = √[(-10)^2 + (0)^2]
AB = √[100 + 0]
AB = √100
AB = 10 meters
Side BC:
Using the distance formula:
BC = √[(-5 - (-5))^2 + (7 - (-2))^2]
BC = √[0^2 + 9^2]
BC = √0 + 81
BC = √81
BC = 9 meters
Side CD:
Using the distance formula:
CD = √[(5 - (-5))^2 + (7 - 7)^2]
CD = √[(10)^2 + 0^2]
CD = √100 + 0
CD = √100
CD = 10 meters
Side DA:
Using the distance formula:
DA = √[(5 - 5)^2 + (7 - (-2))^2]
DA = √[0^2 + 9^2]
DA = √0 + 81
DA = √81
DA = 9 meters
Now, to find the perimeter of the room:
Perimeter = AB + BC + CD + DA
Perimeter = 10 + 9 + 10 + 9
Perimeter = 38 meters
Therefore, 38 meters of crown molding is needed to place around the room.