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) .(1 point) Responses 12 miles 12 miles 12 square miles 12 square miles 8 square miles 8 square miles −12 miles negative 12 miles
To find the length and width of the rectangle, we can use the distance formula between two points. The formula for finding the distance between two points (x1, y1) and (x2, y2) is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For the length of the rectangle:
Length = Distance between points A and B
= √((5-1)^2 + (-3-(-3))^2)
= √(4^2 + 0^2)
= √16
= 4 miles
For the width of the rectangle:
Width = Distance between points B and C
= √((5-5)^2 + (-1-(-3))^2)
= √(0^2 + 2^2)
= √4
= 2 miles
To find the perimeter, we add up all four sides of the rectangle:
Perimeter = 2(Length + Width)
= 2(4 + 2)
= 2(6)
= 12 miles
Therefore, the perimeter of the rectangle is 12 miles.