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 your answer to the nearest whole number. Do not include units in your answer.

Answer 1

`Area = 30`

Explanation:

Given

Rectangle coordinates

`A = (0,4)`

`B = (4,2)`

`C = (1,-4)`

`D =(-3,-2)`

Required

The area of the rectangle

The area is calculated as:

`Area = Length* Width`

The length of the rectangle will be represented as:

`Length = AB = CD`

And the width is:

`Width = BC = AD`

Calculate distance AB using:

`AB = √((x_1 - x_2)^2 +(y_1 - y_2)^2 )`

Where:

`A = (0,4)` ---
`(x_1,y_1)`

`B = (4,2)`
`--- (x_2,y_2)`

`AB = √((0 - 4)^2 +(4 - 2)^2 )`

`AB = √((- 4)^2 +(2)^2 )`

`AB = √(16 +4 )`

`AB = √(20)`

Calculate distance BC using:

`BC = √((x_1 - x_2)^2 +(y_1 - y_2)^2 )`

`C = (1,-4)`
`---(x_1,y_1)`

`B = (4,2)`
`--- (x_2,y_2)`

`BC = √((1 - 4)^2 +(-4 - 2)^2 )`

`BC = √((- 3)^2 +(-6)^2 )`

`BC = √(9 +36)`

`BC = √(45)`

So, the area is:

`Area = Length * Width`

`Area = AB * BC`

`Area = √(20) * √(45)`

`Area = √(20 * 45)`

`Area = \sqrt{900`

`Area = 30`