Question

find the perimeter and area of the rectangle with vertices (-4, 7), (5, 7), (5, 2), and (-4, 2). note that you can draw in the scratch area below, but it is not part of the answer. scratch area (not part of answer)

Explanation:

Step1: Find the length of two - adjacent sides

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For two points $(x_1,y_1)$ and $(x_2,y_2)$.
Let's find the length of the side between $(-4,7)$ and $(5,7)$. Here $x_1=-4,y_1 = 7,x_2 = 5,y_2 = 7$.
$d_1=\sqrt{(5-(-4))^2+(7 - 7)^2}=\sqrt{(5 + 4)^2+0^2}=9$.
Let's find the length of the side between $(5,7)$ and $(5,2)$. Here $x_1 = 5,y_1=7,x_2 = 5,y_2 = 2$.
$d_2=\sqrt{(5 - 5)^2+(2 - 7)^2}=\sqrt{0+( - 5)^2}=5$.

Step2: Calculate the perimeter

The perimeter $P$ of a rectangle is given by $P=2(l + w)$, where $l$ and $w$ are the length and width of the rectangle.
$P=2(9 + 5)=2\times14 = 28$ units.

Step3: Calculate the area

The area $A$ of a rectangle is given by $A=l\times w$.
$A=9\times5=45$ square units.

Answer:

Perimeter: 28 units
Area: 45 square units