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

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

   Hint (a):

   Recall the properties of quadrilaterals. Do any apply to this shape?

2. $ABCD$ is rotated $180°$ about the origin to create $A'B'C'D'$. Then $A'B'C'D'$ is reflected across the $x$-axis to form $A''B''C''D''$. Name the coordinates of $C'$ and $D''$.