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).

Answer 1

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.