if rectangle band has vertices with the coordinates b(-6,0), a(-2,3), n(4,-5), and d(0,-8), find the area of rectangle band. use the keypad to enter the answer in the box provided. the area of rectangle band is square units.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $BA$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $B(-6,0)$ and $A(-2,3)$, $x_1=-6,y_1 = 0,x_2=-2,y_2 = 3$.
$$
\begin{align*}
BA&=\sqrt{(-2+6)^2+(3 - 0)^2}\
&=\sqrt{4^2+3^2}\
&=\sqrt{16 + 9}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step2: Calculate the length of $AN$
For points $A(-2,3)$ and $N(4,-5)$, $x_1=-2,y_1 = 3,x_2=4,y_2=-5$.
$$
\begin{align*}
AN&=\sqrt{(4 + 2)^2+(-5-3)^2}\
&=\sqrt{6^2+(-8)^2}\
&=\sqrt{36+64}\
&=\sqrt{100}\
&=10
\end{align*}
$$
## Step3: Calculate the area of the rectangle
The area of a rectangle $A = l\times w$. Here $l = AN = 10$ and $w=BA = 5$.
$A=5\times10$

# Answer:
$50$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(BA\)

Step2: Calculate the length of \(AN\)

Step3: Calculate the area of the rectangle

Answer: