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: Use distance formula for side lengths

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Let $A(-5,-1)$, $B(-2,-1)$, $C(-3,-4)$, $D(-6,-4)$.
The length of $AB$: Since $y$-coordinates are the same ($y_1=y_2 = - 1$), $AB=\vert-2-(-5)\vert=\vert-2 + 5\vert=3$.
The length of $BC$: $x_1=-2,y_1=-1,x_2=-3,y_2=-4$. Then $BC=\sqrt{(-3+2)^2+(-4 + 1)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.16$.

Step2: Use properties of parallelogram

In a parallelogram, opposite sides are equal. So the perimeter $P = 2(AB + BC)$.
$P=2(3+\sqrt{10})\approx2(3 + 3.16)=2\times6.16 = 12.32$.

Answer:

C. 12.32 units