the vertices of a rectangle are listed below. q(6,8), r(8,6), s(2,0), t(0,2) what is the area of the rectangle? a. 24 square units b. 48 square units c. 22.6 square units d. 12 square units

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of side $QR$
Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $Q(6,8)$ and $R(8,6)$, $x_1 = 6,y_1 = 8,x_2 = 8,y_2 = 6$.
$$
\begin{align*}
QR&=\sqrt{(8 - 6)^2+(6 - 8)^2}\
&=\sqrt{2^2+(- 2)^2}\
&=\sqrt{4 + 4}\
&=\sqrt{8}=2\sqrt{2}
\end{align*}
$$
## Step2: Calculate the length of side $RS$
For points $R(8,6)$ and $S(2,0)$, $x_1 = 8,y_1 = 6,x_2 = 2,y_2 = 0$
$$
\begin{align*}
RS&=\sqrt{(2 - 8)^2+(0 - 6)^2}\
&=\sqrt{(-6)^2+(-6)^2}\
&=\sqrt{36+36}\
&=\sqrt{72}=6\sqrt{2}
\end{align*}
$$
## Step3: Calculate the area of the rectangle
The area of a rectangle $A = l\times w$. Here $l = 6\sqrt{2}$, $w=2\sqrt{2}$
$$
\begin{align*}
A&=(6\sqrt{2})\times(2\sqrt{2})\
&=6\times2\times\sqrt{2}\times\sqrt{2}\
&=12\times2\
& = 24
\end{align*}
$$

# Answer:
A. 24 square units

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QUESTION IMAGE

Question

Explanation:

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

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

Step3: Calculate the area of the rectangle

Answer: