Find the perimeter of rectangle ABCD , with vertices A(1,7) , B(4,7) , C(4,−4) , and D(1,−4) .(1 point)
Responses
12 units
12 units
16 units
16 units
33 units
33 units
28 units
The perimeter of a rectangle is found by adding up the lengths of all four sides.
Using the distance formula, we can find the lengths of the sides:
AB = sqrt((4-1)^2 + (7-7)^2) = sqrt(3^2) = 3
BC = sqrt((4-4)^2 + (-4-7)^2) = sqrt(11^2) = 11
CD = sqrt((1-4)^2 + (-4+4)^2) = sqrt(3^2) = 3
DA = sqrt((1-1)^2 + (7-(-4))^2) = sqrt(11^2) = 11
Adding up all the sides:
3 + 11 + 3 + 11 = 28
So, the perimeter of rectangle ABCD is 28 units.