Answer:
The parallelogram ABCD is a square with side length of
\(\sqrt{13}\).
Step-by-step explanation:
The coordinates of the given quadrialteral ABCD are
\(A(3,5)\\B(5,2)\\C(8,4)\\D(6,7)\)
The best way to see which type of quadrilateral is, it's to draw.
The image attached shows the quadrilateral ABCD. According to our figure, it seems to be a square.
To demonstrate that the parallelogram ABCD is a square, we need to find the length of each side.
\(AB=\sqrt{(2-5)^{2} +(5-3)^{2} } =\sqrt{9+4}=\sqrt{13}\)
\(BC=\sqrt{(4-2)^{2} +(8-5)^{2} } =\sqrt{4+9}=\sqrt{13}\)
\(CD=\sqrt{(7-4)^{2} +(6-8)^{2} } =\sqrt{9+4}=\sqrt{13}\)
\(DA=\sqrt{(7-5)^{2} +(6-3)^{2} } =\sqrt{4+9}=\sqrt{13}\)
Therefore, the parallelogram ABCD is a square with side length of \(\sqrt{13}\).
