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what is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
15.3 units
20.4 units
30.6 units
52.0 units

Question

Accepted Answer

# Explanation:
## Step1: Find the length of one side using the distance formula
The distance formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let's assume two adjacent vertices of the rectangle. For example, if we take two points $(-7, - 1)$ and $(-5,4)$
$$
\begin{align*}
d_1&=\sqrt{(-5+7)^2+(4 + 1)^2}\
&=\sqrt{(2)^2+(5)^2}\
&=\sqrt{4 + 25}\
&=\sqrt{29}\approx5.4
\end{align*}
$$
## Step2: Find the length of the other side using the distance formula
Take another two adjacent vertices, say $(-5,4)$ and $(3,2)$
$$
\begin{align*}
d_2&=\sqrt{(3 + 5)^2+(2-4)^2}\
&=\sqrt{(8)^2+(-2)^2}\
&=\sqrt{64+4}\
&=\sqrt{68}\approx8.2
\end{align*}
$$
## Step3: Calculate the perimeter of the rectangle
The perimeter formula of a rectangle is $P=2(l + w)$. Here $l\approx8.2$ and $w\approx5.4$
$$
\begin{align*}
P&=2(8.2+5.4)\
&=2\times13.6\
& = 30.6
\end{align*}
$$

# Answer:
30.6 units

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QUESTION IMAGE

Question

Explanation:

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

Step2: Find the length of the other side using the distance formula

Step3: Calculate the perimeter of the rectangle

Answer: