We have been given a graph having coordinate of 4 points which are : (-2,8), (4,9), (6,-3) and (0,-4).
Question says that they are corner points of the rectangle so we can apply distance formula
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
to find the lenght and width of that rectangle.
[tex]AB=\sqrt{\left(4--2\right)^2+\left(9-8\right)^2}[/tex]
[tex]AB=\sqrt{\left(4+2\right)^2+\left(9-8\right)^2}[/tex]
[tex]AB=\sqrt{6^2+1^2}[/tex]
[tex]AB=\sqrt{36+1}[/tex]
[tex]AB=\sqrt{37}[/tex]
[tex]BC=\sqrt{\left(4-6\right)^2+\left(9--3\right)^2}[/tex]
[tex]BC=\sqrt{\left(4-6\right)^2+\left(9+3\right)^2}[/tex]
[tex]BC=\sqrt{\left(-2\right)^2+12^2}[/tex]
[tex]BC=\sqrt{4+144}[/tex]
[tex]BC=\sqrt{148}[/tex]
[tex]BC=2\sqrt{37}[/tex]
Now to find the area we will multiply length (AB) and width (BC)
Area of the rectangle [tex]=\sqrt{37}\cdot2\sqrt{37}[/tex]
Area of the rectangle =2*37=74
Hence final answer is 74 square units.
