Question

select the correct answer. a parallelogram has vertices at (-5, -1), (-2, -1), (-3, -4), and (-6, -4). what is the approximate perimeter of the parallelogram? round your answers to the nearest hundredth. a. 9.16 b. 12 units c. 12.32 units d. 14 e. 14.32

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Find length of one - side

Let's find the distance between $(-5, - 1)$ and $(-2,-1)$. Here $x_1=-5,y_1 = - 1,x_2=-2,y_2=-1$.
$d_1=\sqrt{(-2-(-5))^2+(-1 - (-1))^2}=\sqrt{(-2 + 5)^2+( - 1+1)^2}=\sqrt{3^2+0^2}=3$.

Step3: Find length of adjacent - side

Let's find the distance between $(-2,-1)$ and $(-3,-4)$. Here $x_1=-2,y_1=-1,x_2=-3,y_2=-4$.
$d_2=\sqrt{(-3-(-2))^2+(-4 - (-1))^2}=\sqrt{(-3 + 2)^2+(-4 + 1)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.16$.

Step4: Calculate perimeter of parallelogram

The perimeter $P$ of a parallelogram with adjacent - side lengths $a$ and $b$ is $P = 2(a + b)$. Here $a = 3$ and $b\approx3.16$.
$P=2(3 + 3.16)=2\times6.16 = 12.32$.

Answer:

C. 12.32 units