Find the perimeter of rectangle ABCD , with vertices A(1,7) , B(4,7) , C(4,−4) , and D(1,−4) .(1 point)
Responses
28 units
28 units
12 units
12 units
33 units
33 units
16 units
To find the perimeter of the rectangle ABCD, we need to find the length of all four sides and add them together.
The length of side AB can be found using the distance formula:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
= √((4 - 1)^2 + (7 - 7)^2)
= √(3^2 + 0)
= √9
= 3 units
The length of side BC can be found using the distance formula:
BC = √((x2 - x1)^2 + (y2 - y1)^2)
= √((4 - 4)^2 + (-4 - 7)^2)
= √(0^2 + (-11)^2)
= √(0 + 121)
= √121
= 11 units
The length of side CD can be found using the distance formula:
CD = √((x2 - x1)^2 + (y2 - y1)^2)
= √((1 - 4)^2 + (-4 - (-4))^2)
= √((-3)^2 + 0^2)
= √(9 + 0)
= √9
= 3 units
The length of side AD can be found using the distance formula:
AD = √((x2 - x1)^2 + (y2 - y1)^2)
= √((1 - 1)^2 + (7 - (-4))^2)
= √(0^2 + 11^2)
= √(0 + 121)
= √121
= 11 units
Now, we can add all four sides together to find the perimeter:
Perimeter = AB + BC + CD + AD
= 3 + 11 + 3 + 11
= 28 units
Therefore, the perimeter of rectangle ABCD is 28 units.