Answer:
The area of the rectangle ABCD is [tex]\frac{2}{5}[/tex] square units.
Step-by-step explanation:
From statement we have that rectangle ABCD is formed by the following points: [tex]A(x,y) = (2, 5), B(x,y) = \left(\frac{8}{3}, 5 \right), C(x,y) = \left(\frac{8}{3}, \frac{28}{5} \right), D(x,y) = \left(2, \frac{28}{5} \right)[/tex]. First, we calculate the length of each side by the Pythagorean Theorem:
[tex]AB = \sqrt{\left(\frac{8}{3}-2 \right)^{2}+ (5-5)^{2}}[/tex]
[tex]AB = \frac{2}{3}[/tex]
[tex]BC = \sqrt{\left(\frac{8}{3}-\frac{8}{3}\right)^{2}+\left(\frac{28}{5}-5\right)^{2} }[/tex]
[tex]BC = \frac{3}{5}[/tex]
[tex]CD = \sqrt{\left(2-\frac{8}{3} \right)^{2}+\left(\frac{28}{5}-\frac{28}{5} \right)^{2}}[/tex]
[tex]CD = \frac{2}{3}[/tex]
[tex]DA = \sqrt{\left(2-2\right)^{2}+\left(5-\frac{28}{5} \right)^{2}}[/tex]
[tex]BC = \frac{3}{5}[/tex]
Which satisfies all minimum characteristics for a rectangle. The area of the rectangle ABCD is the product of its base and its height, that is:
[tex]A = \left(\frac{2}{3}\right)\cdot \left(\frac{3}{5} \right)[/tex]
[tex]A = \frac{2}{5}[/tex]
The area of the rectangle ABCD is [tex]\frac{2}{5}[/tex] square units.
