what is the area of a rectangle with vertices at $(-4,0)$, $(-3,1)$, $(0,-2)$, and $(-1,-3)$? enter your answer in the box. do not round any side lengths. units²

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of one side using the distance formula
The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Let's take the points $(-4,0)$ and $(-3,1)$
$$
\begin{align*}
d_1&=\sqrt{(-3+4)^2+(1 - 0)^2}\
&=\sqrt{1^2+1^2}\
&=\sqrt{1 + 1}\
&=\sqrt{2}
\end{align*}
$$
## Step2: Calculate the length of an adjacent side
Take the points $(-3,1)$ and $(0,-2)$
$$
\begin{align*}
d_2&=\sqrt{(0 + 3)^2+(-2 - 1)^2}\
&=\sqrt{3^2+(-3)^2}\
&=\sqrt{9+9}\
&=\sqrt{18}=3\sqrt{2}
\end{align*}
$$
## Step3: Calculate the area of the rectangle
The area of a rectangle $A = l\times w$. Here $l=\sqrt{2}$ and $w = 3\sqrt{2}$
$$
\begin{align*}
A&=\sqrt{2}\times3\sqrt{2}\
&=3\times2\
&=6
\end{align*}
$$

# Answer:
$6$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of one side using the distance formula

Step2: Calculate the length of an adjacent side

Step3: Calculate the area of the rectangle

Answer: