Find the perimeter of the rectangle with the vertices
To find the perimeter of a rectangle given the vertices, we need to first calculate the length of each side of the rectangle using the coordinates of the vertices.
Let's say the vertices of the rectangle are given as A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4).
Let's assume the vertices of the rectangle are A(1, 1), B(1, 4), C(5, 4), and D(5, 1).
To find the length of each side of the rectangle, we calculate the distance between the points:
AB = √((x2 - x1)^2 + (y2 - y1)^2) = √((1-1)^2 + (4-1)^2) = √(0^2 + 3^2) = √9 = 3
BC = √((x3 - x2)^2 + (y3 - y2)^2) = √((5-1)^2 + (4-4)^2) = √(4^2 + 0^2) = √16 = 4
CD = √((x4 - x3)^2 + (y4 - y3)^2) = √((5-5)^2 + (1-4)^2) = √(0^2 + (-3)^2) = √9 = 3
DA = √((x1 - x4)^2 + (y1 - y4)^2) = √((1-5)^2 + (1-1)^2) = √(-4^2 + 0^2) = √16 = 4
Now, the perimeter of the rectangle is the sum of the lengths of all four sides:
Perimeter = AB + BC + CD + DA = 3 + 4 + 3 + 4 = 14
Therefore, the perimeter of the rectangle with the given vertices is 14 units.