find the perimeter of rectangle ABCD, with vertices A ( -8, 3 ), B ( -1, 3), C ( -1, -6), and D ( -8, -6). A 32 units. B 30 units. C 36 units. D 63 units
To find the perimeter of the rectangle ABCD, we need to add up the lengths of all four sides.
Side AB:
Using the distance formula, we find the distance between points A and B:
AB = √((-1 - (-8))^2 + (3 - 3)^2)
AB = √(7^2)
AB = 7 units
Side BC:
Using the distance formula, we find the distance between points B and C:
BC = √((-1 - (-1))^2 + (-6 - 3)^2)
BC = √(9^2)
BC = 9 units
Side CD:
Using the distance formula, we find the distance between points C and D:
CD = √((-8 - (-1))^2 + (-6 - (-6))^2)
CD = √(7^2)
CD = 7 units
Side DA:
Using the distance formula, we find the distance between points D and A:
DA = √((-8 - (-8))^2 + (3 - (-6))^2)
DA = √(9^2)
DA = 9 units
Now, we add up all four sides to find the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 7 + 9 + 7 + 9
Perimeter = 32 units
Therefore, the perimeter of rectangle ABCD is 32 units. So the correct answer is A) 32 units.