Apply the techniques of using the coordinates to find the length and the width of the polygon. Use the length and the width to find the perimeter of the polygon in miles. Rectangle ABCD has vertices point A (1,−3), point B (5, −3), point C (5, −1), and point D (1, −1).
Responses
−12 miles
12 miles
12 square miles
8 square miles
To find the length and width of the rectangle, we need to find the distance between points A and B (which is the length) and the distance between points A and D (which is the width).
Using the distance formula:
Length AB = sqrt[(5-1)^2 + (-3-(-3))^2] = 4 miles
Width AD = sqrt[(1-1)^2 + (-1-(-3))^2] = 2 miles
To find the perimeter, we add up all four sides:
Perimeter = AB + BC + CD + AD = 4 + 2 + 4 + 2 = 12 miles