A restaurant is building an outside seating area. The owner created a map with the coordinates A(−11,11) , B(−3,11) , C(−3,1) , and D(−11,1) . Each unit on the coordinate plane represents 1 foot. Solve to find out how many feet of wall material they will need to build the new area (the perimeter).(1 point)
Responses
40 feet
40 feet
36 feet
36 feet
52 feet
52 feet
80 feet
To find the perimeter of the outside seating area, we need to find the lengths of each side and add them together.
Side AB:
The x-coordinate of point A is -11 and the x-coordinate of point B is -3. The difference between these two x-coordinates is -3 - (-11) = -3 + 11 = 8. So the horizontal distance between A and B is 8 feet.
The y-coordinate of point A is 11 and the y-coordinate of point B is also 11. So the vertical distance between A and B is 11 - 11 = 0 feet.
The length of side AB is the square root of the sum of the squares of these distances: √(8^2 + 0^2) = √(64 + 0) = √64 = 8 feet.
Side BC:
The x-coordinate of point B is -3 and the x-coordinate of point C is also -3. So the horizontal distance between B and C is 0 feet.
The y-coordinate of point B is 11 and the y-coordinate of point C is 1. The difference between these two y-coordinates is 11 - 1 = 10. So the vertical distance between B and C is 10 feet.
The length of side BC is the square root of the sum of the squares of these distances: √(0^2 + 10^2) = √(0 + 100) = √100 = 10 feet.
Side CD:
The x-coordinate of point C is -3 and the x-coordinate of point D is -11. The difference between these two x-coordinates is -3 - (-11) = -3 + 11 = 8. So the horizontal distance between C and D is 8 feet.
The y-coordinate of point C is 1 and the y-coordinate of point D is also 1. So the vertical distance between C and D is 1 - 1 = 0 feet.
The length of side CD is the square root of the sum of the squares of these distances: √(8^2 + 0^2) = √(64 + 0) = √64 = 8 feet.
Side DA:
The x-coordinate of point D is -11 and the x-coordinate of point A is also -11. So the horizontal distance between D and A is 0 feet.
The y-coordinate of point D is 1 and the y-coordinate of point A is also 11. The difference between these two y-coordinates is 11 - 1 = 10. So the vertical distance between D and A is 10 feet.
The length of side DA is the square root of the sum of the squares of these distances: √(0^2 + 10^2) = √(0 + 100) = √100 = 10 feet.
The perimeter is the sum of the lengths of all sides: 8 + 10 + 8 + 10 = 36 feet.
Therefore, the restaurant will need 36 feet of wall material to build the outside seating area.