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

Answer:

$Area = 30$

Step-by-step 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:

$AB = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }$

Where:

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

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

$AB = \sqrt{(0 - 4)^2 +(4 - 2)^2 }$

$AB = \sqrt{(- 4)^2 +(2)^2 }$

$AB = \sqrt{16 +4 }$

$AB = \sqrt{20}$

Calculate distance BC using:

$BC = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }$

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

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

$BC = \sqrt{(1 - 4)^2 +(-4 - 2)^2 }$

$BC = \sqrt{(- 3)^2 +(-6)^2 }$

$BC = \sqrt{9 +36}$

$BC = \sqrt{45}$

So, the area is:

$Area = Length * Width$

$Area = AB * BC$

$Area = \sqrt{20} * \sqrt{45}$

$Area = \sqrt{20 * 45}$

$Area = \sqrt{900$

$Area = 30$