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

Step-by-step 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|=√((4-0^)^2+(2-4)^2)=√(16+4)=√(20) \\ Similarly \\ |CD|=√(20) \end{gathered}`

Then

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

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

`length* breadth=√(20)*√(45)=√(900)=30`

Therefore, the area is 30