the vertices of a rectangle are listed below. u(-3,4), v(-2,3), w(-5,0), x(-6,1) what is the area of the rectangle? a. 6 square units b. 11.3 square units c. 12 square units d. 3 square units

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of side $UV$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $U(-3,4)$ and $V(-2,3)$, $x_1=-3,y_1 = 4,x_2=-2,y_2=3$.
$$
\begin{align*}
d_{UV}&=\sqrt{(-2+3)^2+(3 - 4)^2}\
&=\sqrt{(1)^2+(-1)^2}\
&=\sqrt{1 + 1}\
&=\sqrt{2}
\end{align*}
$$
## Step2: Calculate the length of side $VW$
For $V(-2,3)$ and $W(-5,0)$, $x_1=-2,y_1 = 3,x_2=-5,y_2=0$.
$$
\begin{align*}
d_{VW}&=\sqrt{(-5 + 2)^2+(0 - 3)^2}\
&=\sqrt{(-3)^2+(-3)^2}\
&=\sqrt{9+9}\
&=\sqrt{18}=3\sqrt{2}
\end{align*}
$$
## Step3: Calculate the area of the rectangle
The area of a rectangle $A = l\times w$. Here $l = 3\sqrt{2}$, $w=\sqrt{2}$
$$
\begin{align*}
A&=\sqrt{2}\times3\sqrt{2}\
&=3\times2\
&=6
\end{align*}
$$

# Answer:
A. 6 square units

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QUESTION IMAGE

Question

Explanation:

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

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

Step3: Calculate the area of the rectangle

Answer: