Question

What is the perimeter of a rectangle with coordinates A (1, 7), B (8, 7), C (8, -3), and D (1, -3)?A35 unitsB68 unitsC70 unitsD34 units

Answer 1

Given:

There are given that the coordinates of the rectangle are:

$\begin{gathered} A:(1,7) \\ B:(8,7) \\ C:(8,-3) \\ D:(1,-3) \end{gathered}$

Explanation:

To find the value of the perimeter of the rectangle, first, we need to find the distance between all sides by using the distance formula:

So,

First find the distance for side AB:

$\begin{gathered} AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ AB=\sqrt{(8-1)^2+(7-7)^2} \\ AB=\sqrt{(7)^2+0} \\ AB=7 \end{gathered}$

Then,

For side BC:

$\begin{gathered} BC=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ BC=\sqrt{(8-8)^2+(-3-7)^2} \\ BC=\sqrt{100} \\ BC=10 \end{gathered}$

Then,

For the side CD:

$\begin{gathered} CD=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ CD=\sqrt{(1-8)^2+(-3+3)^2} \\ CD=\sqrt{(-7)^2+0} \\ CD=7 \end{gathered}$

And,

For the side DA:

$\begin{gathered} DA=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ DA=\sqrt{(1-1)^2+(-3-7)^2} \\ DA=\sqrt{(100)} \\ DA=10 \end{gathered}$

Then,

From the formula of perimeter of rectangle;

$P=AB+BC+CD+DA$

Then,

$\begin{gathered} \begin{equation*} P=AB+BC+CD+DA \end{equation*} \\ P=7+10+7+10 \\ P=14+20 \\ P=34units \end{gathered}$

Final answer:

Hence, the correct option is D.