Question

John was visiting four cities that form a rectangle on a coordinate grid at A(0, 4), B(4, 2),C(1, -4) and D(-3, -2). What is the area of the space that cities enclose? Round youranswer to the nearest whole number. Do not include units in your answer.

Answer 1

Explanation

We are given the coordinates of a rectangle as A(0, 4), B(4, 2), C(1, -4), and D(-3, -2).

To get the area of the rectangle,

We will have

So, we can get the area by finding the lengths of adjacent sides and multiplying

$\begin{gathered} |AB|=\sqrt{(4-0^)^2+(2-4)^2}=\sqrt{16+4}=\sqrt{20} \\ Similarly \\ |CD|=\sqrt{20} \end{gathered}$

Then

$\begin{gathered} |DA|=\sqrt{(0-3)^2+(4-(-2))^2}=\sqrt{3^2+6^2}=\sqrt{9+36}=\sqrt{45} \\ Similarly \\ |BC|=\sqrt{45} \end{gathered}$

Therefore, the area of the cities the spaces enclose will be

$length\times breadth=\sqrt{20}\times\sqrt{45}=\sqrt{900}=30$

Therefore, the area is 30