Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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.

Sagot :

Answer:

[tex]Area = 30[/tex]

Step-by-step explanation:

Given

Rectangle coordinates

[tex]A = (0,4)[/tex]

[tex]B = (4,2)[/tex]

[tex]C = (1,-4)[/tex]

[tex]D =(-3,-2)[/tex]

Required

The area of the rectangle

The area is calculated as:

[tex]Area = Length* Width[/tex]

The length of the rectangle will be represented as:

[tex]Length = AB = CD[/tex]

And the width is:

[tex]Width = BC = AD[/tex]

Calculate distance AB using:

[tex]AB = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }[/tex]

Where:

[tex]A = (0,4)[/tex] --- [tex](x_1,y_1)[/tex]

[tex]B = (4,2)[/tex] [tex]--- (x_2,y_2)[/tex]

[tex]AB = \sqrt{(0 - 4)^2 +(4 - 2)^2 }[/tex]

[tex]AB = \sqrt{(- 4)^2 +(2)^2 }[/tex]

[tex]AB = \sqrt{16 +4 }[/tex]

[tex]AB = \sqrt{20}[/tex]

Calculate distance BC using:

[tex]BC = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }[/tex]

[tex]C = (1,-4)[/tex] [tex]---(x_1,y_1)[/tex]

[tex]B = (4,2)[/tex] [tex]--- (x_2,y_2)[/tex]

[tex]BC = \sqrt{(1 - 4)^2 +(-4 - 2)^2 }[/tex]

[tex]BC = \sqrt{(- 3)^2 +(-6)^2 }[/tex]

[tex]BC = \sqrt{9 +36}[/tex]

[tex]BC = \sqrt{45}[/tex]

So, the area is:

[tex]Area = Length * Width[/tex]

[tex]Area = AB * BC[/tex]

[tex]Area = \sqrt{20} * \sqrt{45}[/tex]

[tex]Area = \sqrt{20 * 45}[/tex]

[tex]Area = \sqrt{900[/tex]

[tex]Area = 30[/tex]

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.