Answer:
The parallelogram ABCD is a square with side length of
[tex]\sqrt{13}[/tex].
Step-by-step explanation:
The coordinates of the given quadrialteral ABCD are
[tex]A(3,5)\\B(5,2)\\C(8,4)\\D(6,7)[/tex]
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.
[tex]AB=\sqrt{(2-5)^{2} +(5-3)^{2} } =\sqrt{9+4}=\sqrt{13}[/tex]
[tex]BC=\sqrt{(4-2)^{2} +(8-5)^{2} } =\sqrt{4+9}=\sqrt{13}[/tex]
[tex]CD=\sqrt{(7-4)^{2} +(6-8)^{2} } =\sqrt{9+4}=\sqrt{13}[/tex]
[tex]DA=\sqrt{(7-5)^{2} +(6-3)^{2} } =\sqrt{4+9}=\sqrt{13}[/tex]
Therefore, the parallelogram ABCD is a square with side length of [tex]\sqrt{13}[/tex].
