Respuesta :
Given:
A(1,-1), B(5,-3), C(7,1), and D(3,3)
Area of ABCD = 20.25 square units
Let's determine if the area is correct.
Since ABCD is a square, all side lengths are equal.
Now, let's find the length of one side.
Apply the distance formula:
[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]Let's find the length of AB.
Where:
(x1, y1) ==> A(1, -1)
(x2, y2) ==> B(5, -3)
Thus, we have:
[tex]\begin{gathered} AB=\sqrt{(5-1)^2+(-3-(-1))^2} \\ \\ AB=\sqrt{4^2+(-3+1)^2} \\ \\ AB=\sqrt{16+(-2)^2} \\ \\ AB=\sqrt{16+4} \\ \\ AB=\sqrt{20} \end{gathered}[/tex]The length of one side of the square is √20.
Now, to find the area of a square, we have:
[tex]\begin{gathered} Area=l^2 \\ \\ Area=(\sqrt{20})^2 \\ \\ Area=20\text{ square units} \end{gathered}[/tex]Therefore, the area of the square is 20 square units.
This means the area is not 20.25 square units.
Therefore, the
