On graph paper, plot and connect the points $A(1,1),B(2,3),C(5,3),$ and $D(4,1)$ to form quadrilateral $ABCD$.  

1. What is the best name for quadrilateral $ABCD$? Justify your answer.

   Hint (a):

   Explain why it is not a rhombus.

   Answer (a):

   $ABCD$ is a parallelogram because opposite sides are parallel.

2. Determine $m∠DAB$ and $m∠BCD$. What is their relationship?

3. Write the equations of $\overleftrightarrow { A C }$ and $\overleftrightarrow { B D }$. Are the diagonals of $ABCD$ perpendicular?

   Hint (c):

   Find the slope of each diagonal.

4. What are the coordinates of the intersection point of diagonals $\overleftrightarrow { A C }$ and $\overleftrightarrow { B D }$?