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: Calculate the length of one pair of sides

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for the points \((-5,-1)\) and \((-2,-1)\).
Since \(y_1=y_2=-1\), \(d=\vert x_2 - x_1\vert=\vert-2-(-5)\vert = 3\)

Step2: Calculate the length of the other pair of sides

Use the distance formula for the points \((-2,-1)\) and \((-3,-4)\)
\(d=\sqrt{(-3 + 2)^2+(-4 + 1)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1 + 9}=\sqrt{10}\approx3.16\)

Step3: Calculate the perimeter of the parallelogram

The perimeter \(P = 2(a + b)\), where \(a = 3\) and \(b\approx3.16\)
\(P=2(3 + 3.16)=2\times6.16 = 12.32\)

Answer:

C. 12.32 units