Rectangle ABCD has vertices point A (−5, 1) , point B (−2, 1) , point C (−2, 6) , and point D (−5, 6) . Find the perimeter of the rectangle in feet.
To find the perimeter of the rectangle, we need to calculate the distance between each pair of consecutive vertices and then add them all up.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances for each side of the rectangle:
1. Side AB:
distance_AB = sqrt((-2 - (-5))^2 + (1 - 1)^2) = sqrt(3^2 + 0) = 3 feet
2. Side BC:
distance_BC = sqrt((-2 - (-2))^2 + (6 - 1)^2) = sqrt(0 + 5^2) = 5 feet
3. Side CD:
distance_CD = sqrt((-5 - (-2))^2 + (6 - 6)^2) = sqrt(3^2 + 0) = 3 feet
4. Side DA:
distance_DA = sqrt((-5 - (-5))^2 + (6 - 1)^2) = sqrt(0 + 5^2) = 5 feet
Now, we add up all the distances to get the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 3 + 5 + 3 + 5
Perimeter = 16 feet
Therefore, the perimeter of the rectangle ABCD is 16 feet.