Quadrilateral $ABCD$ has coordinates $A(3, 2)$, $B(1, 6)$, $C(5, 8)$, and $D(7, 4)$.  

1. Graph $ABCD$ on graph paper. What shape is $ABCD$? Justify your answer.

   Hint (a):

   Use the Pythagorean Theorem to find the length of the each side. What does this tell you about the shape?
   Calculate the slope of each side. What does that tell you about the adjacent sides?

2. $ABCD$ is rotated $180º$ about the origin to create $A^\prime B^\prime C^\prime D^\prime$. Then $A^\prime B^\prime C^\prime D^\prime$ is reflected across the $x$-axis to form $A^{\prime\prime} B^{\prime\prime} C^{\prime\prime} D^{\prime\prime}$. Name the coordinates of point $C^\prime$ and point $D^{\prime\prime}$.

3. What are the area and perimeter of $ABCD$?