Find the perimeter of rectangle ABCD , with vertices A(−8,3) , B(−1,3) , C(−1,−6) , and D(−8,−6) .
To find the perimeter of rectangle ABCD, we need to add the lengths of all four sides.
First, let's find the length of sides AB and CD:
AB = √[(-1 - (-8))^2 + (3 - 3)^2]
= √[7^2 + 0^2]
= √49
= 7
CD = √[(-1 - (-8))^2 + (-6 - (-6))^2]
= √[7^2 + 0^2]
= √49
= 7
Next, let's find the length of sides BC and DA:
BC = √[(-1 - (-1))^2 + (-6 - 3)^2]
= √[0^2 + (-9)^2]
= √81
= 9
DA = √[(-8 - (-8))^2 + (-6 - 3)^2]
= √[0^2 + (-9)^2]
= √81
= 9
Now, we can calculate the perimeter:
Perimeter = AB + BC + CD + DA
= 7 + 9 + 7 + 9
= 32
Therefore, the perimeter of rectangle ABCD is 32.