Find the perimeter of rectangle ABCD , with vertices A(−8,3) , B(−1,3) , C(−1,−6) , and D(−8,−6) .(1 point) Responses 63 units 63 units 36 units 36 units 32 units 32 units 30 units
To find the perimeter of the rectangle ABCD, we need to calculate the distance between each pair of adjacent vertices and then sum them up.
The distance formula between two points (x1,y1) and (x2,y2) is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Now, let's calculate the distance between each pair of adjacent vertices:
1. Distance between A(-8,3) and B(-1,3):
Distance AB = √((-1 - (-8))^2 + (3 - 3)^2)
Distance AB = √(7^2 + 0)
Distance AB = √49
Distance AB = 7 units
2. Distance between B(-1,3) and C(-1,-6):
Distance BC = √((-1 - (-1))^2 + (-6 - 3)^2)
Distance BC = √(0 + 9^2)
Distance BC = √81
Distance BC = 9 units
3. Distance between C(-1,-6) and D(-8,-6):
Distance CD = √((-8 - (-1))^2 + (-6 - (-6))^2)
Distance CD = √(-7^2 + 0)
Distance CD = √49
Distance CD = 7 units
4. Distance between D(-8,-6) and A(-8,3):
Distance DA = √((-8 - (-8))^2 + (3 - (-6))^2)
Distance DA = √(0 + 9^2)
Distance DA = √81
Distance DA = 9 units
Now, sum up the distances of all sides to get the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 7 + 9 + 7 + 9
Perimeter = 32 units
Therefore, the perimeter of rectangle ABCD is 32 units.