a parallelogram is graphed on a coordinate plane with vertices a(-5, -5), b(-4, 0), c(2, 0), and d(1, -5). what is the perimeter of the parallelogram? round the answer to the nearest tenth. enter the answer in the box. units

Question

a parallelogram is graphed on a coordinate plane with vertices a(-5, -5), b(-4, 0), c(2, 0), and d(1, -5). what is the perimeter of the parallelogram? round the answer to the nearest tenth. enter the answer in the box.   units

Accepted Answer

# Explanation:
## Step1: Calculate the length of side $AB$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $A(-5,-5)$ and $B(-4,0)$, $x_1=-5,y_1 = - 5,x_2=-4,y_2 = 0$.
$$
\begin{align*}
AB&=\sqrt{(-4+5)^2+(0 + 5)^2}\
&=\sqrt{1^2+5^2}\
&=\sqrt{1 + 25}\
&=\sqrt{26}\approx5.1
\end{align*}
$$
## Step2: Calculate the length of side $BC$
For $B(-4,0)$ and $C(2,0)$, $x_1=-4,y_1 = 0,x_2=2,y_2 = 0$.
$$
\begin{align*}
BC&=\sqrt{(2 + 4)^2+(0-0)^2}\
&=\sqrt{6^2}\
&=6
\end{align*}
$$
## Step3: Calculate the perimeter of the parallelogram
In a parallelogram, $AB = CD$ and $BC=AD$. The perimeter $P=2(AB + BC)$.
Substitute $AB\approx5.1$ and $BC = 6$ into the formula:
$$
\begin{align*}
P&=2(5.1+6)\
&=2\times11.1\
&=22.2
\end{align*}
$$

# Answer:
$22.2$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of side \(AB\)

Step2: Calculate the length of side \(BC\)

Step3: Calculate the perimeter of the parallelogram

Answer: