Find the perimeter of rectangle ABCD , with vertices A(1,7) , B(4,7) , C(4,−4) , and D(1,−4) .
To find the perimeter of rectangle ABCD, we need to calculate the sum of the lengths of all four sides.
First, calculate the length of AB:
AB = sqrt((4-1)^2 + (7-7)^2) = sqrt(3^2 + 0^2) = sqrt(9 + 0) = sqrt(9) = 3
Then, calculate the length of BC:
BC = sqrt((4-4)^2 + (-4-7)^2) = sqrt(0^2 + (-11)^2) = sqrt(0 + 121) = sqrt(121) = 11
Since AB and CD are parallel and have the same length, the length of CD is also 3 units.
Lastly, calculate the length of AD:
AD = sqrt((1-1)^2 + (-4-7)^2) = sqrt(0^2 + (-11)^2) = sqrt(0 + 121) = sqrt(121) = 11
Now, sum the lengths of all four sides to find the perimeter:
Perimeter = AB + BC + CD + AD
Perimeter = 3 + 11 + 3 + 11
Perimeter = 28
Therefore, the perimeter of rectangle ABCD is 28 units.