rectangle abcd has coordinates a(2,1), b(1,3), c(-5,0), and d(-4,-2). find the area of the rectangle.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $AB$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $A(2,1)$ and $B(1,3)$, $x_1 = 2,y_1 = 1,x_2 = 1,y_2 = 3$.
$$
\begin{align*}
AB&=\sqrt{(1 - 2)^2+(3 - 1)^2}\
&=\sqrt{(-1)^2+2^2}\
&=\sqrt{1 + 4}\
&=\sqrt{5}
\end{align*}
$$
## Step2: Calculate the length of $BC$
For $B(1,3)$ and $C(-5,0)$, $x_1 = 1,y_1 = 3,x_2=-5,y_2 = 0$.
$$
\begin{align*}
BC&=\sqrt{(-5 - 1)^2+(0 - 3)^2}\
&=\sqrt{(-6)^2+(-3)^2}\
&=\sqrt{36+9}\
&=\sqrt{45}=3\sqrt{5}
\end{align*}
$$
## Step3: Calculate the area of the rectangle
The area of a rectangle $A = l\times w$, where $l = BC$ and $w = AB$.
$$
\begin{align*}
A&=\sqrt{5}\times3\sqrt{5}\
&=3\times5\
& = 15
\end{align*}
$$

# Answer:
The area of rectangle $ABCD$ is $15$.

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(AB\)

Step2: Calculate the length of \(BC\)

Step3: Calculate the area of the rectangle

Answer: